If I'm actually sick enough to be home from work (almost never) I'm not going to be playing games. I'll either be sleeping it off or lying down on the sofa watching a movie. Passive forms of entertainment have their place when you're not feeling well.
"Whether you think you can, or you think you can't, you're right." -Henry Ford
I'm rarely sick as well, but when i do get sick it tends to be really bad. That said, i still forge on with whatever game i was already playing at the time. For example if i got sick right at this moment it would be Record of Agarest War.
Elf this....Elf that....I'll Elf your mother. Yuki Nagato FTW
If it's the former, I usually lay in bead, try to play anything but wind up putting on Netflix and passing out. If it's the latter, Star Wars: Old Republic or something else I can sink a lot of time into in a single day.