We play in bed. DS is 4 so I can trust he won't get himself into trouble if I doze off. But we bring toys, books, snacks into bed and play "lazy bears" for the day.
We nurse a lot. Make forts on the bed, play with flashlights. Play board games. Listen to books on CD.
Now that he is older, I would put in a DVD if I felt desperate because I was ill. But I never did for the first 3.5 years and I truly try NOT to default to that.
In fact, the one time this winter I decided to do a movie when DS was sick (the rule normally is we never do movies during the daylight hours. It's only a night time treat once or twice a month for family movie night) Well after I made the mistake of saying "well you're really sick so we will watch a movie together this afternoon." Once he was healthy, he would come up to me and (in his best bad acting) say "Mom I think I am sick so can we watch a movie during the day?" HA! I don't think so buddy!
Also DH is very supportive and if I am sick as a dog he will take the time off work so I can rest and that way DS is not cooped up with me going stir crazy.
We were all 3 sick a few times this winter... and we just basically did our normally rainy day inside activities, but did most of them in bed as mentioned above. We all mope around and feel sorry for ourselves and try to get the dog to cook dinner and know that even though the situation sucks, this too shall pass.
As I have said before here on this forum, while I don't think it's a crime for kids who are older (3.5-4+) to watch a carefully selected DVD either for fun with the family or in odd situations like long plane trips or sickness... I think the MISTAKE is creating an atmosphere where the media distraction is EXPECTED and relied upon. They need to know how to get through things like plane trips of sick days without plugging in. It should be a treat, not a necessity.