Arkham City is the best game of the year this year, usurping 3-way tie between Portal 2, Mortal Kombat, and Bastion. Its open-world, fluid combat, sandbox approach to stealth encounters, and general tone make the game shine to a polish the likes of which I haven't seen in a game. There are an amazingly low amount of bugs for a game with this much content, and the game is a blast to play from beginning to end.
The Catwoman levels add a lot of variety to the gameplay, granted you'll need to buy the game New if you don't want to swing by the PSN/XBL Marketplace for the pack. Catwoman is extremely fun to play in her own little plot, and getting the Catwoman-specific Riddler Trophies is a great extra challenge.
I suggest getting Batman Arkham Asylum before AC for two reasons: It's one of the greatest games to release in 2009, and for the small bit of key backstory present in the Riddler challenger and Amadeus Arkham recordings.
To put it bluntly, I thought the real GOTY fight would be between Skyrim and Uncharted 3, but a new player has entered the ring, Arkham City.
I read a few reviews for this game as well as watching it be played. It's probably the most accurate Batman simulator that I've seen, and I think it's probably one of the best games of the year. haha I'm not going to say it' the best until Skyrim comes out.