Are there smartphones which support Android and, in addition to it, some other operating systems, in particular Symbian and RIM Blackberry? Or, maybe, the last two are constrained to devices which don't support Android?
RIM only make Blackberry OS for their own specially-designed hardware, they don't release their OS to be installed on other people's hardware. However the new Blackberry Playbook (running their brand new QNX OS) can run Android apps as well as Blackberry apps, I don't think there are any phones running their new OS yet, but they will be coming soon. So that could do some of what you want to do with dual booting?
Phones designed for Symbian often have much lower hardware specs than ones designed for Android, so you're going to struggle to get Android running on them. See this previous question Is it possible to get Android on a Nokia e65?
Phones designed for Windows Mobile and Windows Phone 7, however are a different matter. They do (mostly) have high enough specs, and a lot of the time are almost identical hardware-wise to Android phones from the same manufacturer. In these cases all that is needed is for someone to spend some time gathering (or writing) Android hardware drivers for the specific hardware in the phone, and then porting an Android build onto them. There are a few websites that co-ordinate projects to get Android running on these phones, XDA Devs being one of the biggest.
See this previous question which does overlap with this one by quite a bit Can I install Android on my non-Android device?
In practical terms, there are no Android phones that support other popular operating systems, because the other OSs are closed source. A possible exception is, for example, the HTC HD2; it's almost identical to the HTC Desire Z, and Android can be run on it, so it's entirely possible that ripping Windows Mobile 6 from the HD2 and flashing it on a Desire Z would work.
As GAThrawn notes, the reverse (getting Android onto other phones) has been done; check out Can I install Android on my non-Android device? for that.
The phones doesn't support an operating system, It's the OS that support the phone. You can run any OS on a smartphone as long as someone ports the OS to that phone