
Got inspiration for this question as I was glancing over an immersion watch an ex had gifted me while we were dating. Not as fancy as the ones I usually wear, but I like it for its compactness and kept it over the years.
I mean, there's no reason to throw away an useful gift even if we broke up. My wife once enquired about it and was fine with it.
I think that unless they are extremely sentimental gifts, it's silly to throw them away or want our partner to throw them away because they were gifted during a past relationship.