What NFS have you been playing? I loved NFS Hot Pursuit. The Run was... okay. Most wanted I rather liked, the new one, Rivals I wasn't super into, but I know people have liked it. Even NFS Shift and Shift 2 are fun, but are more simulation than arcade (which the above titles are). Burnout Paradise is an older one but a great one to try if you like NFS Most Wanted. The DiRT series too I enjoyed, they're rally racers, but very fun still. Midnight Club LA is kind of fun, not as much as the above mentioned tho (IMO).

GTA is a king all it's own, but Saint's Row 3 and 4 are very fun takes on that genre. They're super cheesy with outrageous adult humor tho (instead of super serious like GTA).

You list skyrim, have you played Oblivion? Same series, 1 game before. Slightly different feel, but just as addictive.

With Borderlands, there's 2 to choose from. I feel Dead Island is kind of like those games, it's more melee focused tho. Still slaughtering for XP and new weapons tho, has similar kind of 4 player co-op as Borderlands.

Beyond that, here's a few I highly recommend:

The Saboteur - Not well know, it's a third person open world game like GTA, only set in WWII, Nazi occupied France in the 40s. Starts off black and white and gets color as your liberate areas from the nazis. I loved this game.

The Last of Us - A little slower, but a wonderfully atmospheric game set in a world where a fungus has taken over most of humanity, making some of us zombie-like mindless drones. This one's a ride for sure.

Spec Ops: The Line - A third person military shooter... but with a heavy hitting story. It's controls are tight as hell and it was a blast to go through.

I also agree with Ahamm002 about Bioshock infinite. Actually, all 3 bioshock games are great, infinite included.