Day 13 - favourite character arc
The team grows up
Honorable mentions: Morgan as team leader, but unfortunately, that arc was dropped just when things were beginning to get interesting.
This is a tough one to answer because CM isn't really a character-driven show (although its characters are more fleshed-out than most crime shows) and there aren't a whole lot of arcs to choose from. This answer is kind of a cheat because it involves the team as a whole and not just one character (although the character most significantly affected is probably Hotch).
I covered most of this already with my Hotch essay on Day 2, so I'll spare you a detailed explanation this time. But those episodes from the ending of season 2 into the beginning of season 3 are still among my favorites, because I loved the way the strength of the team was tested. Other finales have been incredibly intense and suspenseful (in that regard, "Lo-Fi" and "Mayhem" are standouts) but "Doubt" into "In Name and Blood" really got to the heart of the characters, and remain some of the most powerful television I've seen. I've talked about my take that Gideon's departure was an unexpected boon for the narrative--it really propelled it forward in a great direction. Granted Gideon's letter was a bit too Meredith Grey for my tastes, but the really great stuff comes when the team deals with his departure. Hotch, especially, seems to take it hard, not only because Gideon was a trusted friend, but because he's also aware that it falls to him now to fully lead this team. This is important, because despite his holding the position of team leader since season one, the narrative itself clearly favors Gideon, and the rest of the team looks up to him as the voice of authority and wisdom. Even Hotch, to an extent, defers to his experience and expertise. Now it's Hotch who steps into that role.
And as I explained in my Hotch essay, stepping into that role is not without sacrifice. Hotch's character undergoes his most profound changes in season 3, because it's here that he fully commits to the mission--that like Gideon, he becomes the mission. His transition into Gideon's role signals with the end of his marriage. Strauss tells him he now has no hope of promotion beyond the BAU; he accepts this. And we are left wondering if he will become like Gideon eventually--jaded, broken-down, alone. The rest of the team grows up as well--they seem a little tougher, a little wearier, a little harder--but their bond is also stronger than its ever been; Prentiss has proven her loyalty and cemented her place within this family. It's not the happiest of arcs, but it is very powerful, and definitely signals a major turning point in the series.