I am rewatching films on a regular basis, and not only films I previously enjoyed. It has something to do with observing how your tastes and perceptions change overtime, as well as the fact that i think every work of art deserves multiple viewings for its full appreciation. 
In fact I've been rewatching more films in the past few months than watching new ones.
If you want to rewatch 20 movies in during the next few weeks, I'd suggest that you choose from some categories:
a) films you really want to see again
b) personal favorites
c) films you are not sure you have "grasped"
d) films you forgot you saw them
e) films about which you may change your opinion on a rewatch (in which direction is another question)
f) films you didn't like, but which others consider worthwhile.

I'm sure there are more possibilities, but I can't think of them right now. 
Would be great if you could talk a bit about your feelings and experiences when you have rewatched some movies and are able to compare the two experiences of it.