I think this is a "case-by-case-basis" sort of issue, but the question you should always ask is "Why am I doing this?"
I get what PPs have said about returning engagement/wedding rings because they are a symbol of a promise that is no longer going to be fulfilled. Gifts are, well, gifts. They remind you of the giver, but they are yours. They are not (or at least should not be) given with the expectation of return. If that was true you would call it a loan, not a gift. Unless they ask for it, I don't see a way to return a gift to an ex without symbolically throwing it in their face. I think it is also nearly impossible to ask for a gift back without coming off as bitter/petty etc.
I have broken up with my best friend since childhood, and she was in the middle of helping me redo my house. Now I hate the room she helped paint, and I don't want to hang up the lamps she bought me. I would return them if she asked for them but otherwise I will probably give them away. If I decide to keep the big picture she bought me for my living room as an "early Xmas present," I may perform a cleansing ritual to reclaim is as "mine" instead of "the picture she gave me." Sounds silly I know. But that's what I'd have to do to find peace.
My friend and I have swapped back things we've loaned each other, everything else was a gift that we have to deal with on our own. I will do whatever I need to do with what I own via her, but I will do it alone and for myself. Whatever choices I make about the objects in my life have to be about me, for me, and by me. That is the only way for me to find closure. Whether I keep her gifts or give them away, I need to own the choice.