My vote is for "watch". Don't be tricked by "except" (which would suggest a gerund)... the keyword is "do". "I can do nothing except watch TV." I did a quick search, and interestingly the results which gave "do nothing except watching" were often full of other terrible mistakes.

You need "except" here. It's like using "but" : I can do nothing except/but watch TV. (I'd use "but" rather than "except" but that is just personal preference).

The latter, i.e. "watching". It is called "gerund", you can check it out. http://en.wikipedia.org/wiki/Gerund

"I can do nothing except watch TV." Sometimes substituting another verb can clarify which form you should use. For example, "I can do nothing except play." "I can do nothing except read." "I can do nothing except work." "I can do nothing except clean." Using "-ing" in any of these sentences sounds awkward.