'lo g_rob :-)
There's lots and lots going on in the amiga scene. Your options for your regulation dose of amiga experience are many.
There are
Classic 680x0 based amiga systems - the 1200, 4000 etc. You can generally expand these quite heavily and run the latest 680x0 version of the amiga os (v3.9). You can fit faster processors, extra ram, graphics cards, PCI expansion busses etc. to these to build a very capable system.
PowerPC amiga systems - A1200 or A4000 with PPC processor cards (these are the earliest examples of PPC amigas), AmigaOne and Pegasos 1/2.
The latter are fully PPC based machines, using a minimum G3 processor, AGP/PCI busses etc. on an ATX compatible motherboard. The AmigaOne is the "official" successor to the classic line and AmigaOS4 is being developed for it (still in beta phase).
The Pegasos (there is actually a pegasos 2 also) is a clone system that has been in development a bit longer and runs its own OS called "MorphOS", (technically still a beta too) which is quite mature and I believe offers very good OS3.x compatibility.
Both use emulation to support 680x0 software transparently.
Unfortunately there is quite some friction between the above platforms, which is pretty unfortunate given their obvious similarites. It's difficult to get into a discussion about these systems without it triggering a flame fest, so be careful ;-)
Next up there is AROS. The feller who first responded to your post is the guy to ask about that! It's an effort to create a cross platform AmigaOS, although I believe its fair to say it's presently most advanced on x86 systems.
Lastly there are emulations of classic 680x0 systems. Theres UAE, Amithlon etc. UAE is a standalone application that has come an amazingly long way since it first appeared.
Systems like Amithlon are related but they (IIRC) can be run on top of a mimimum bootstrap so you effectively have OS3.x booting on your PC (or whatever).