1. Read A Book
What could be better than cozying up on the couch with a blanket, a cup of tea/coffee/hot chocolate, and a good book? Reading in a pool of sun is nice, too, but there's something about staying inside picking up where you left off in a great story, or starting one from scratch, when the sky is gray and rain is coming down.
2. Go See a Movie
That said, going out in the rain isn't that bad either, provided the roads aren't too dangerous. Again, you can get that cozy feel being inside, and finding a new story, only this time on the big screen. And if the nearest theater is still too far away, or a bit too expensive, maybe you can find a Redbox.
3. Bake Something
I love to bake, especially when it's cloudy and dark outside; chocolate chip cookies are my favorite (and my family's), but brownies, cakes, pies, etc. are delicious, too. Only downside is having to clean up afterwards, but at least you can lick the beater then.
4. Play A Game
Anyone up for Scrabble? I know physical games aren't in style much anymore, but maybe you can bring them back. I'm sure you have a bunch of board games in your closet somewhere, or a deck of cards in your drawer. So bring them out and see where a little friendly competition can take you.
5. Binge Watch
Watching TV is also a great way to spend a rainy day, since you can't really go outside anyway; it's the perfect time to catch up on all your shows, or maybe find a new one. It should be easy, what with Netflix, Comcast On Demand, marathons on channels like USA and TNT...I think it's best with a friend or family member, if you both like the same thing.
6. Entertain Your Pet
I know my dog is always ready to play, and doesn't care what the weather's like. If it is too wet to take Fido for a walk, then you can still play with their squeaky toys/tennis balls/tug ropes. It's a great bonding experience, and gets you both a little exercise (which you're gonna need if you also baked something).