I discovered this by accident. All of our faucets are chrome, and we have soft water that leaves deposits on the finish. I used Kaboom cleaner (CLR or some other mineral-removing product would work, too) and a nonscratch Scotchbrite pad to get the mineral crust off.

Then, use polish meant for glass cooktops (I used MAAS brand) to polish and buff with a soft cloth. The polish is mildly abrasive, and has silicone, so it resists water marks and fingerprints.

I did the kitchen faucet this morning, and I swear, it looks like new. No scratches, no water marks!