Can you quit a side quest in Assassin’s Creed 2

There's two rewards to collecting the Feathers. With 50, you unlock a special hammer weapon. At 100, you unlock the Auditore Cape, which makes you Notorious.

and just an Achievement or Trophy. Bragging rights really.

No, you don't get any rewards for the side quests other than the fact that you get closer to 100% sync -- if that's what you want.

If you read the contract mission statements a bit closely, you'll notice that there is some relation to the overall story, though not much.

Most of all though, they're fun. The contract missions are great fun because you get to try out some of the more exotic techniques. I still remember the first time I assassinated from a bench. It was hilarious when Ezio sat him down on the bench behind him.

Try a few, then decide if you want to do them all or skip.

EDIT: Oh, I forgot the cash rewards for side missions. But it's easy to forget cash in AC2, since you have way more than you'll ever need.