See under the cut for a theory about the Grimm tradition not being some sort of ability, but a modern fairytale curse.
Spoiler light, mostly for Pilot and Bears Will Be Bears, and some minor ones for Three Coins in a Fuchsbau.
So... about that curse.
As Grimm progressed through its season, I found more and more that the mantle of Grimm seemed to appear like some sort of bizarrely modified blood curse. Look at its operating parameters: Every generation of a Grimm family is systematically marked for death; first the oldest child, and then their younger sibling, and then their younger sibling, until finally the entire generation is annihilated and the curse moves on to ravage the next generation. We have no way of knowing if Kelly and Marie are unusual for Grimms, although they seem to not be entirely out of the ordinary, but they both died remarkable young. Far from being a boon, this seems to operate exactly like a fairytale curse; Marie calls it all but that in the pilot: 'the misfortune of our family has passed on to you'.
Fairytale justification for this concept is rife, but no more so than in the tale of Sleeping Beauty, both the original Grimm version and the Disneyfied version. Most of us know the story, actually, a child is born and several fairies come from far and wide to bestow blessings on the girl, she's awesome, she's amazing, she's perfect. The story goes downhill from there, however, an evil fairy - either because she was not invited or did not find the party to her standards - cursed Sleeping Beauty to prick her finger on a spinning wheel and die. All was not lost for Sleeping Beauty however - or else she would have been labeled 'Dead Beauty' or perhaps 'Zombie Beauty'; there is one remaining fairy who has not yet bestowed her blessing, and although she cannot undo the wicked fairy's curse, she could modify it and bring hope to it. Sleeping Beauty would not die, she would fall asleep, and she could be awoken by the kiss of a Prince. Huzzah.
I think it is possible something similar is at work with the Grimms. Grimms - their entire line, really - has been blessed with heightened physical abilities, uncanny deductive reasoning, and various other perks. Nick and Hank comment on this within the first five minutes of the Pilot: Hank mentions that Nick has always had a knack for knowing the truth of someone he looks at on the street, profiling them effortlessly. So we know this is not a new ability that Nick acquired when Aunt Marie became deathly ill. Actor interviews have also suggested that the entire Grimm line has heightened abilities, and David Giuntoli has said that some Grimm families train nearly from birth for their fate, so they must also be capable of believing in Wesen, unlike a 'normal' human brain. There are clearly several perks from being descended from the Grimm line that have nothing to do with their Wesen-fighting powers.
But what about the Grimm mantel itself? I believe it is a curse. I believe the entire line has been fated to be killed at the hands of Wesen; even Marie, who has been dying of cancer, does not finally pass until one last attack by a Wesen tips her over the edge. That is the curse that was laid down on the House of Grimm ages ago.
The modification of that curse is that Grimms will see it coming. That every new Grimm will be imbued with whatever additional powers seem to have fallen to Nick after his Aunt Marie died. When he tries, Nick seems to be able to force Wesen to reveal themselves to him so he can be prepared for his attack. His combat skills appear to have been bumped up several notches. In short, the final fairy modified the curse to give the Grimm line a fighting chance.
Monroe informs Nick that 'Nick's kind' began profiling Wesen approximately 200 years ago. Was that due to a desire to hunt down bad Wesen, or a proactive defense mechanism to see who would come after them and how to handle them? The Brothers Grimm (or at least it is strongly implied to be them) have turned their family curse into a blessing of sorts, a way to insure that their descendants live for as long as possible and have the tools to fight. That is the only mitigation for the Grimms: they know what is coming and how to face it and they do not have to lay down for their fate.
It's possible that the true nature of the curse has been lost. Maybe Marie herself didn't know of the true terms of the curse, but maybe she did. She breaks up with Farley as soon as she becomes the Grimm, and even though Farley does not appear to be 'one of the bad ones' them dating in the first place was controversial among her family. Who would invite a Wesen into their home and confidence if they knew they were fated to die at the hands of Wesen? Mornoe and Nick's friendship (Nick and Rosalie's friendship, Nick and Bud's friendship) could never have begun unless Nick did not know the full scope of the curse. Perhaps that was the piece of information that Renard desperately did not want Nick to know for some reason.
Repercussions:
There is likely a 'curse ender' built somewhere in the curse. This is a fairytale after all; this is a potential (sadish, I would say) ending to the entire series. Nick breaks the curse that is the misfortune of his family and goes off into the sunset a perfectly normal human being, no longer plagued with the curse that his haunted his family for generations.
Almost all Wesen fear Grimms. Why? Because all Grimms are trained, out of necessity for survival, to kill Wesen. Everyone in the series expresses surprise when Nick helps a Wesen out of a jam. He steps in between beavers and trolls, in between wolves and pigs, and no one expects that of him. It's just the way it always has been that Grimms lord over Wesen, kill them no matter what their crimes, and leave them to their own petty disputes.
Stretch Repercussions:
I've seen it theorized (and considered myself) the idea that Nick (and all Grimms) are actually members of the royal line - whether they are human or some other sort of Wesen with no Face. Depending on how the curse travels, it is entirely possible that Grimm-ness is a curse on one of, or several of the distaff royal lines. This would potentially mean that some of the fundamental positives of the Grimm heritage (acute observational skills/heightened physical abilities) are actually items that are in all of those in the royal line, with the Grimm curse or without.
Issues:
How are there so many Grimms?! This has all the ear-marks of a textbook fairytale curse and yet there are at least a few other Grimms out there. Were several lines cursed at once? Have previous Grimms found a way to stretch their curse across to family members? Are multiple branches of the same family cursed separately? We know there was at least one Japanese Grimm - which surprised our European Grimm. When did the curse originate?
Grimm Blood - is the 'fatal' nature of Grimm blood to Hexenbeasts (and perhaps other Wesen?) a function of the Grimm curse, or the cause of it? This seems to be a metaphorical invocation made literal: 'it is in your blood to defeat them'. Are pre-Grimms toxic to Hexenbeasts as well?
How does the curse travel? We have seen the curse go from Kelly to Marie and then to Nick, eradicating at least one branch of the Kessler line (save Nick). Does Kelly and Marie's Grimm parent have a sibling? Does that sibling have children? If the answer to these questions is 'yes' then it tells us interesting things about the course of the curse. It appears that the curse travels primarily along the main line, and might not jump over to the distaff line for several generations. When Nick dies (hopefully not for a very long time!) would his Grimm line die out or would it travel to a distant cousin?
Why do some Wesen work with the Royal Houses? Are the Houses human or Wesen? If they are human it makes exceptional sense that they would work with the Families as a matter of survival; they are unlikely to be killed directly by a Royal House member if that is the case.
Conclusion:
Obviously there is insufficient information to say for certain, but the idea of a curse being the cause of Nick's powers is classic fairytale. Regardless of whether or not something like this comes to pass I think it's an interesting theory. Any nitpicks or additional elements that support or contradict the theory are welcome.