Pretty sure that light weight is one of the hallmarks of expensive steel, not cheap steel.
Sometime ago there was a thread about determining gold content. I posted this as a simple way of measuring density, needing only a glass of water, a skewer, a ruler, some thread and some aluminium foil. My experience was that you can get remarkably good estimates of density this way. Get something close to 4.5 and there is a good chance it is Titanium.
However there are claims of cheap alloys that are as low as 10% Ti. If there is a lot of aluminium in the alloy it might be hard to tell from the density alone as there is scope to build an alloy of Titanium, Aluminium and Iron that could have the right density, and the right lustre.
If it were my ring, I would stick it in the scanning electron microscope I use at work, and use energy-dispersive X-ray spectroscopy (EDS) to perform elemental analysis. 
Yes, there are nondestructive testing methods, if you have access to them. EDS, X-Ray Fluorescence, which uses the same principle, but without the microscope, or X-Ray Diffraction.
We’ll… I’ll have to get myself down to Radio Shack and get one of those.
Sure, what do you have in mind?
Not sure exactly, but you might be able to do some sort of scratch test, or something like that.
I suppose we should also ask if the ring has any setting, or if it’s just all metal, since a setting would complicate the density method.
Google says iron corrodes in sulfuric and hydrochloric acids, while titanium does not. No idea of the details though, or if that would make a practical test.
ETA: I have a few pieces here of either surgical stainless steel or titanium, and I wouldn’t mind minor damage to a portion of it to find out which it is. So if there’s a test that’s easily done at home I could give it a try. Don’t have a dremel though.
Titanium does corrode in strong acids, and a bit in diluted hydrochloric. That’s what keeps it from being noble.
How about trying to anodize it? You only need coke and a 9V battery: Titanium in Technicolor I think you should be able to polish off the coating if you don’t want it.
Has anybody mentioned trying to sell it at a pawn store or junkyard and having them analyze it for you? 
There’s a much simpler way to perform Positive Material Identification:
http://www.niton.com/en/metal-and-alloy-analysis/applications/pmi