My husband and I play euros all the time- games like Carcassone, Kingdom Buiider, Dominion, Dominant Species, as well as backgammon and cards. He is a master chess player and plays extremely complicated war games, so nothing too competitive or it isn't any fun and as he also has phenomenal luck I would always lose. The Euros are designed to come out fairly even, there is a strategy element, but also a random one. They are very absorbing, and some, like kingdom builder are very difficult and a good check on whether the drugs have started to kill off my brain cells. I can always beat him at backgammon, but our set came from Syria and he is convinced it favors me, as my grandparents were born there.
My son is always trying to get me to play more complicated video games, but I have trouble coordinating the controls. I do enjoy simple things like bejeweled and Angry Birds. He plays D&D as my husband did when we were teenagers, and we have started playing Arkham Horror as a family.
I agree completely that games are a wonderful distraction from the pain. I find new needlework projects extremely absorbing, but I am afraid that my interest lags after a bit and I finish fewer than I start. Most of the fun is in the planning!