I've tried cleaning cymbals with several of the methods mentioned - Magic Eraser (abrasive, leaves residue), Zildjian polish (polishes, obviously), soap and water (does nothing), and I've been disappointed every time, so I don't do it anymore. I like my cymbals to look new, so now I mostly just buy new or mint-condition cymbals when I need one. It costs me more money, but not a LOT more - cymbals hold their value quite well. If I have one that gets nasty-looking for some reason, I'll sell it and get a new one, but that generally doesn't happen because I handle my cymbals carefully. I lift them by the edges or by putting my finger underneath the hole. I even do cymbal chokes by putting my palm to the edge of the cymbal so I don't cover it with fingerprints. A dry microfiber cloth will get rid of most stick marks, but fingerprints are pretty much permanent.
I wish I wasn't so particular about it, I see other drummers eating fried chicken and then doing 5-finger cymbal chokes without a care in the world, and they look so happy. But I can't let anyone touch my cymbals.
I wish I wasn't so particular about it, I see other drummers eating fried chicken and then doing 5-finger cymbal chokes without a care in the world, and they look so happy. But I can't let anyone touch my cymbals.