I'm a Pirates season ticket holder, so most of my collection is is related to them.
I have a game-worn jerseys from Josh Bell and Tyler Glasnow that I'm hoping to get framed soon and then a ton of autographed balls from guys over the last decade or so (McCutchen, Marte, Taillon, Cole, etc.). A cool item I have is a lineup card from one of the games that my friends and I attended during my bachelor party in '14 when we were playing the Nats in DC signed by most of the guys that played that night (Marte, Polanco, Melancon, Burnett, etc.) and Clint Hurdle. Most had a good laugh when I talked about the back story behind it.
My favorite item is a game-used ball from the game that A.J. racked up his 2,000th strike out that he signed for me. I know he likely isn't a favorite of Yankees fans, but we absolutely love him in Pittsburgh...easily one of my favorite Pirates of all-time alongside some of the early 90's guys (Van Slyke, Bonilla, Varsho) from when I was a young kid.
Beyond that, I have a Steelers helmet signed by Ben, AB, and Le'Veon that is pretty cool.
As for UConn stuff, I have an 8 x 10 that Calhoun signed for me as I was leaving the trainers room in Gampel one morning while I was in school. My wife bought me a framed picture of Kemba for Christmas that is signed along with "2011 Champs" which I always point out when my Pitt fan friends are over.