@ Tomoyo -- I just found out in our current SGOTM that renegotiating peace locks you into a second peace treaty (or war declaration) even if renegotiate deals is off. Stinks, if you ask me, especially since the second treaty is offered straight up. (Presumably if you renegotiated peace the first time, it was because you could get the AI to give you something for it.)
Letting expired treaties go on is rarely in your favor, unless it's a situation like Pentium said where you *know* you're going to declare shortly. The AI will only allow the trade to go on in the first place if it's currently in their favor -- in other words, if they don't show up asking to cancel, it means you're paying too much (or they're paying too little).
Renata