You don't necessarily need one of the upcoming smartphones with 3D displays in order to get a 3D-like effect from your phone, at least not if you check out the upcoming 3DBoard app for jailbroken iPhones.
While most people associate a 3D display with the stereoscopic illusion of depth, just as key is the ability to see "around" objects when shifting your point of view. Typical 3D display setups don't bother with this aspect of vision, as it would require elaborate head-tracking, wouldn't be suitable for pre-rendered content like movies, and wouldn't support more than one viewer per screen. On the flip side, all those caveats start to disappear when you're dealing with something the size of a smartphone; the Nintendo DSi title Looksley's Line Up is a prime example of making it work.
3DBoard uses your iPhone's sensors, rather than head tracking, to estimate the phone's orientation in regards to your eyes. With this information it can pull of a subtle but impressive effect, shifting the icons on the phone's home screen ever so slightly in regards to the background, making it appear as if they float just over it. Someone else using your phone may not even notice what's changed at first glance, aside from a feeling that your iPhone just looks different from any other they've ever used.
Author Apocolipse is finishing up work on this tech demo now, and expects to add 3DBoard to Cydia's jailbroken app store in the near future.