Near is actually much more complicated than he appears to be on the surface. Because of how popular L is, many fans (myself included), tend to automatically discount Mello and especially Near on their first read. Near is thus seen as a poor substitute for L, childish, cold, and immature, and probably the least desired to obtain the final victory.
Or at least, that was my first impression of him. But then I kept reading, and went back and read again. And really, to discover Near's character, that is what's required. On the surface, he really is those things I've listed in a lot of ways. Near is a very rational person, with the ability to understand and process the situation around him at a rapid rate. Thus he is able to control his emotional responses in an extreme sense, to the point of appearing not to have them at all. He has a short temper when it comes to not being understood, as well as for people and actions he considers unsavory. He's very blunt and to the point, not mincing words based on social perceptions or acceptability. He's almost always seen either playing with toys or stacking things, reinforcing the idea of him being childish, and moreover he often mistreats the toys, taking them apart and at some points, breaking them. And, as Light puts it, he becomes so focused on the total and perfect victory over Kira that he almost in fact loses to him in the end. All these things add up to giving the impression I previously listed, but at the same time, can be the doorway into revealing much much more.
One of the most obvious things about Near is his utter inability to function on his own. It comes up in HTR13 as a statistic, and is evidenced in the series when Near has Rester fly all the way from Japan to New York just so he can accompany Near on the trip back to Japan. There is no other deeper reason presented for this; Near just doesn't want to make travel arrangements or fly alone. I think ultimately for Near, the inability to care for himself would simply be defined as a lack of caring about things everyone else considers necessary tasks. Bathing, brushing his teeth, changing his clothes, laundry, preparing food, eating, sleeping...all of those things take time to do and even to remember. Near, however, is thinking so much about everything else, that he just forgets to do these things. Moreover, if he were to try on his own, he'd forget halfway through. Food would be left to burn and laundry to sour. These things aren't important, something that was potentially strengthened by a childhood in Wammy's House, where they would've likely been taken care of for Near as Watari takes care of L.
Near in a lot of ways lives in his own head. His ability to process information and understand what's going on around him is extraordinary, too much so for his brain to be able to effectively communicate with the world outside of him. It's like a huge tank of water trying to leak out of a pinhole. It puts enormous pressure and anxiety on the tank, in this case, Near himself, to have to get that information out. This is something he's dealt with his whole life, and I think in a lot of ways, his answer to this is toys. Throughout the series, especially when he uses the finger puppets and block dolls, Near fiddles with his toys as he talks, and often has them acting out what he's saying. It's a physical manifestation of his thoughts, and I think the way he has found for himself to be able to communicate. Physically acting out his thoughts in a sense slows them down, as it is naturally more time consuming than just saying them. In this way he's actually trying to effectively communicate with those around him, and in most cases, it works. However, he is frustrated when it doesn't, smashing toys into his Lego walls, for example. It can be seen as arrogance, but Near's patience is in ways tried every time he opens his mouth. He can't just think and have people understand; he has to slow down for them. I think that's why he sees himself as being above them, but not in a prideful sense. It's merely the reality for him, even if others don't perceive it that way.
And at the same time, these communication difficulties present their own problems. Social interactions become a royal pain in the ass when a person has to go through this frustration every single time he opens his mouth. In terms of my own speculation, I've defined a reason in his childhood, when his parents literally gave up on him because they couldn't handle him. Near's ability to understand made it seem like he had little emotional reaction, but the truth was that this was devastating for him. It was irrefutable proof that not only was he different, but that difference drove people away. Instead of finding answers for themselves, they just gave up, and thus gave him up. This makes it even more difficult for Near to form connections, for fear that the same thing will happen again, and why go through that frustration only to have it go to painful waste? The rational choice would be not to force himself to endure what he's already got problems enduring. However, whatever the ultimate reason, there is canon evidence to support the theory, as in Near's own words he admires people who are willing to do anything to achieve their goals, such as L and Mello. In the special after-series one-shot, Near openly says that learning this about L marks the reason and the time in which he began to respect him, despite having been in Wammy's house for some time at that point. These people will stop at nothing, including the law, in order to win, and Near admires that. That mutual drive, emphasized in Wammy's House to an almost insane degree as shown in the novel "Another Note," becomes the bond for people like Near and Mello, who is the most real embodiment of this drive for Near.
While Mello sees Near as his rival, I think Near has a very different opinion of Mello, and of people he will meet like him. Near is able to recognize qualities in others that he lacks in himself. Unlike Mello, Near wanted to work together from the very start, when they first heard of L's death. I think this was because he knew Mello could do things that Near couldn't. And at the same time, I don't think Near ever figured out how to express that in a way that Mello would see as believable or anything beyond pity. What to Near is simple truth, to Mello is almost a slap in the face; Near is well aware that in the aspects they are praised for in Wammy's House, he will always be superior. But at the same time, Near knows that outside Wammy's House, Mello can accomplish so much more. It's just unfortunate that what goes on outside doesn't count in the game.
Of course, a lot of this is based on assuming that Near likes both Mello and L. It was speculated by the artist of the manga that Near actually didn't like L, and thus made his finger puppet ugly. I actually disagree with this; Near had never seen L, only heard descriptions of him at best, and this could easily explain the distortions. Moreover, two of Near's most powerful emotional responses come in the aftermath of L's and Mello's deaths respectively. In the case of L, Near dumps his puzzle, and says that if they lose, they are losers. I've touched on Near using his toys to communicate, and this is no different. The almost complete puzzle which is otherwise blank save for an L falls apart, just as L's case did by his death. While it's not necessarily for the person, I think Near was emotionally impacted by L's death, and this shows it.
A more convincing case can actually be made in the case of Mello's death. When Hal first tells him, Near simply tells her not to worry, and that the problem has been solved. The next time the matter is brought up by Near is in the Yellow Box Warehouse, as he says it's thanks to Mello that Near has won. The single panel is one of the most important in showing Near's personality, because it shows that he is not a cold and heartless bastard. In this one panel, Near is deliberately drawn with his eyes covered by his hair. There is only one other panel that I've found where the same thing is seen, at a moment of important revelation regarding how they will defeat Kira. Usually Near's eyes are always very deliberately focused away from anyone he is talking to, and always seen. But in this scene, where he has actually been making significant eye contact because it is the moment of his triumph, Near's eyes are covered from not only the reader, but from Kira. I think this is because Near knew that something could be seen in them as he spoke of Mello. Gratitude, sadness, remorse...any of these could be seen as weakness, and in that particular moment, weakness couldn't be allowed. And in truth, I think it was all of these that were lurking there. Near not only couldn't save Mello, but his own short-sightedness in some ways caused Mello's death. Near feels guilty because of this, because he lost the person who in so many ways was the completion of his abilities, and who, in his own words, he could stand with and surpass even L. I also think this is because he's lost the one person in his life who literally would never give up on him--or at least, give up on surpassing him. Mello embodies this desire perhaps even more than L did. Mello would kill anyone, while L stuck to killing criminals. And while he thought it was wrong, Near could in fact understand it.
I mentioned eye contact, and think it should be brought up again because it goes to Near's awkwardness in social situations, and also his confidence. As I mentioned, Near doesn't make deliberate eye contact with any person throughout the series, save on two occasions. He also purposely avoids eye contact when facing a person on one notable occasion, which will come later. The two times he makes eye contact are when he is talking to Mogi in the SPK headquarters, and when he is confronting Light at the Yellow Box Warehouse in the final meeting. During the first of these occasions, Near is imitating L, asking Mogi to do whatever it takes to solve the Kira case, even at risk of his own life. While Near had no way of knowing that L had posed this same ordeal to Mogi and the others before, Near was likely going off what he had heard described, either by Mello or some other child from Wammy's House who had seen L. In the second instance, which is far more important, Near makes no real effort to hide his eyes from anyone. This scene is of course, the moment of Near's triumph over Kira, when he has the absolute proof and the perfect victory even L couldn't obtain. Considering that the series prior Near spends in speculation and efforts to reach this goal, I think it's significant. In this one instance, Near seems completely unafraid of even the strangers around him. He is confident and without doubt of any sort, because he knows that he and Mello together have won. I think that only when Near has this surety is he able to maintain prolonged eye contact. From this, it can be speculated that Near doubts himself a fair bit, at least when it comes to talking to people. This was of course, addressed earlier, but bears repeating, as the eye contact is an important part of his character.
Then comes the one time we seem him deliberately avoid eye contact. Usually Near is not facing the person he's talking to either, but in this case, when he returns Mello's picture to him, Near turns towards the older man, yet averts his eyes. Even being Mello, or rather, especially since it is Mello, I think this again speaks to his confidence in social interaction. Mello is important to Near, and yet Near still can't bring himself to meet his eyes, even when he faces him. And Mello, who takes offense at almost everything Near says and does, isn't insulted by this! I think it's because in this one instance, Mello and Near both know that it's not about Near being superior, but in fact a sign of Near's inability socially. It's not a major enough weakness that if pressed Near would break down, but it is in fact a lack of confidence in this one area, and a recognition again of his own shortcoming. I think it is also important to note that if Near finds someone less than human, such as Kira, I think he would have a much easier time making eye contact with them than he would with normal people, and even more so, people that he likes and cares for.
Note, however, at this confidence only applies in the areas of social and life skills. When it comes to intelligence, Near is very sure of himself.
Then we come to the matter of morality, something that I think is a central part of every Death Note character. Near, in my mind, is without a doubt an objectivist. He acts rationally in every situation, and thinks for himself. He says openly at the end of the series that if a god does exists, and puts his teachings before Near, he would study it, and then decide for himself if it was right or wrong. This goes to one of the fundamental points of objectivism, in that a person should never blindly accept any faith, and certainly no idea without proof. And we see Near's morality in his actions; it is in fact one of the things that makes him less than L, because he will not test the Death Note. Though he speaks of killing people in the series by legal means (such as the death penalty), Near himself is not directly responsible for any death that can be proven. Matsuda speculates in the final chapter that Near actually tested the Death Note on Mikami to ensure that he would win, but if such was the case, Near would be a complete and superior "L" without the need for Mello. Because of his unwillingness to test the Death Note that created the situation that would have led to his death had Mello not acted, and also because of the one-shot set 3 years later where Near still considers what L would do for a significant period of time before he acts, I doubt this is the case. Instead, I agree with Ide that it's what Matsuda wishes because he did like Light. Though in the future perhaps Near will become the sort of person who can do such things, at this time with his personality, Near is against his hand being the one to kill. At the same time, however, he can understand killing, and even how it would make a person normal to do so, such as if someone found the Death Note and tried it a time or two.
However, Near's morality certainly doesn't put him above lying to people, at least when it has a purpose. He intentfully deceives Aizawa and the others by claiming Kira has killed Mogi so that they will more easily make up their minds to offer him information. In turn, when Aizawa does call, Near immediately tells him the truth, and explains his actions, which even Aizawa sees the justification for. On the other hand, Near isn't so opposed to lying that he doesn't enjoy it in some ways either. When he lies to Kira in particular, about capturing Mello and his subsequent escape, and also about Mogi, Near is smiling. I think this goes hand in hand with the other times we see Near smile, and that's when he's doing something clever, and also when he knows he's right. Near enjoys being right, largely because, well...who doesn't? And considering that in his life, the one thing he is routinely praised for and is in fact considered the best at is his deductive reasoning and logical skills, he has all the more reason to be happy over it, despite that other people might consider him wrong for doing it.