I considered Titanium and Tungsten Carbide, since I'm allergic to all flavors of gold. But BrokenMa and I wanted our bands to match, and her engagement ring was white gold. So mine's platinum.
The Ti rings are nice, but they lack a decent "heft", which is aesthetically displeasing to me (they feel like plastic toys out of a quarter-machine at the grocery store). The TC ones are nice and heavy and look a lot like hematite, which I think is really cool.
One thing to keep in mind with either of these newfangled ring materials is this: They can't be resized, ever. So if you gain or lose a significant amount of weight, the ring would have to be replaced instead of adjusted.
Ti can't because there's no way to resize it without leaving a visible seam, and TC because it's not really a metal as much as it is a sintered ceramic, so it can't bend at all without fracturing. At least that's my understanding.
-BP