Even though my dad cheated on my mum and broke her heart, I see her engagement ring and wedding band as a "symbol" of the time they were happiest - they were together for 13 years and there are a lot of wonderful memories of that time that I have and that both my mum and dad have too and regularly talk about... I think it really depends why you broke up and what your time together was like...

I have kept mine - originally I kept them in case DS wanted them for some reason but the older he gets and as his understanding grows of what my time was like with XDH and what his time now is like with his dad, I don't see him wanting anything to do with them.
Their "symbol" is very toxic so I'm considering having them cleaned and polished and then selling them...