Lots of devices support IPv6. My last 2 Androids have and I can go onto this website via my Galaxy Nexus and IPv6 over Wifi now. The carriers need to show initiative here and get IPv6 rollout underway. Nearly all have been really slack in this regard.
Not nearly enough though. Some recent Android builds do, but not all. The Galaxy SIII doesn't let you select it, for example. We didn't have a lot of success with iOS 5, although in theory it is supported. Lots of Symbian S60 devices do it fine, but there are none left in the market. Windows phones -- well, we've heard of them *cough*.
The bottom line is it's nowhere near well enough supported on a broad enough range of devices to be released to the unwashed masses.