This is a bit of a tough one.
#1 is simple, it's Dark Souls. It's my favourite game for a reason.
The second spot is a bit harder but I'll start with removing the easy ones:
-Batman: Arkham City just didn't live up at all to its predecessor and I really dislike the fact that they went open world with it.
-Portal 2 is a masterclass in design but I would call it more "interesting" than "compelling" as a game experience.
-Rayman: Origins just isn't my cup of tea, sorry.
-Minecraft may have officially released in 2011 but let's face it, it was cool long before that.
-Uncharted 3 is one half good game and one half trash cover-based third-person shooter. Not good enough.
-Mortal Kombat is a fighting game and I feel like they live and die by their scene, the gameplay itself is rarely the biggest experience.
So it's down to either Skyrim or Deus Ex. Both I played for many hours, both I enjoyed a great deal.
#2 will probably have to be Skyrim, if only for the legacy it left behind, if you can even call it a legacy, the game is pretty much still alive and well.