I would repot the basil and cut it in half. You can root the cuttings in a pot of soil. Your parsley looks healthy. Has it been windy there?

They're indoor windowsill plants actually. I just had them outside while I was moving some stuff around.

I would harden them off and leave them outside. The basil could be cut back and personally I'd eat the cut off part.

So I threw the basil and parsley back on my windowsill and the basil straightened itself out. The parsley is still tilted over, but seems like it's becoming more upright as well. Do I still need to do anything about the height or will it stop growing eventually on its own?

The Basil definitely needs cutting down a bit so it starts to branch more. I'd be eating it up as fast as it could grow. Cut it just above where the two branches come out and watch what happens.