MorphOS has OS4Emu which can run some (but not all) PowerPC AmigaOS4 software. It also runs other PowerPC Amiga software (WarpOS and PowerUP were already mentioned). There are also plenty of native MorphOS ports of Amiga software.
If you just want to try classic 68k Amiga software and games on modern hardware, check out the variants of UAE. WinUAE for Microsoft Windows is, unfortunately, far superior to other versions. Cloanto provide a commercial package called Amiga Forever which includes WinUAE, licensed ROM files and most models of Amiga ready to emulate out-of-the-box. For the free UAE, you'll either need to obtain Amiga ROM files (which are still under copyright, hence illegal to download), or try out the free ROM replacement based on AROS (a version of this is included with WinUAE and some other UAE variants).
For old games, WHDLoad can also speed up loading times by removing the need for floppy disks (real or emulated), though this also costs money for unrestricted use. WHDLoad works on real Amiga hardware as well as UAE (including MorphOS UAE).
Also, UAE only has JIT-compilation on x86 processors (regular PCs), so it's a lot slower on PowerPC. There is currently a bounty proposed to bring JIT-compilation to PowerPC UAE, for both OS4 and MorphOS (and Linux on PPC), however this doesn't seem to have gotten very far yet.
MorphOS uses transparent 68k emulation using JIT compilation (more efficiently than UAE), but this doesn't work for software which uses the original Amiga chipset. The MorphOS version of UAE lacks JIT, so won't be the fastest emulated Amiga, although is fine for many old games.
At the moment, OS4 only runs on extremely overpriced and underpowered hardware. MorphOS looks the better choice if you want a PowerPC-based Amiga-like system, preferably on a compatible old Mac. Registering MorphOS is not very cheap though, but still a much cheaper option than running OS4.
The unofficial Moana CD will get a very limited AmigaOS 4.0 desktop running on a Mac Mini G4 (1.5GHz/64MB VRAM model only, AFAIK). It's not really usable though.
There is also a port of AROS to PowerPC, as a nightly build. On a Mac Mini G4, this has to be run under Linux (e.g. a dual-boot of Debian or Ubuntu), and is pretty limited and unstable from my experience with it.
For x86 PCs, as well as UAE/WinUAE/Amiga Forever (for emulated 68k software), there are also distributions of AROS such as Icaros Desktop, which run natively or in a virtual machine. These are free, fast, can run UAE, but are not as developed as MorphOS or OS4 (which are both PPC-only), and won't work natively on all PCs.
That seems to have covered most modern Amiga options.
[ Edited by Mequa 14.06.2012 - 01:17 ]