I think the above comments have actually covered everything worth knowing!!!
But to summerise:
Amiga Inc. are making (contracting) a new PPC based motherboard, they have done the same with AmigaOS, which is being ported as we speak by Hyperion. Hyperion state that the project is in a quite advanced state, but this has not been demonstrated to the public yet. Hyperion also claim to be having problems running 68k (original) Amiga programs in the new OS at the moment, due to emulator problems. Does not attempt to emulate Amiga custom hardware.
MorphOS is a new OS designed to run on another PPC based motherboard called Pegasos. MorphOS is not finished, but can run 68K code. The Pegasos board with an early version of MorphOS is avaiable to buy now, with future updates to the OS free (IIRC). Some AROS code has been used in this project. Does not attempt to emulate Amiga custom hardware.
AROS is a free AmigaOS clone, it was written from scratch to the original AmigaOS specifications. It is portable to virtually any CPU and/or architecture, notably x86 and 68k at the moment (with limited PPC, ARM, etc.. work already done). It does not attempt to run 68K code on non 68K systems. When run on an Amiga it can replace AmigaOS without the user being aware of this. Any existing AmigaOS C source code should run fine on it. AROS is not finished yet. Does not attempt to emulate Amiga custom hardware.
All three project are great, and have chose totally different paths to achive an AmigaOS style environment. AmigaOS and MorphOS are compeating in the PPC market and are comercial (you have to pay for them).
While most of the AROS development has been for the x86 (Athlon, Pentium etc..) and the Palm hand-held device, with the dev team looking at the Athlon64. AROS is non comercial (free to download and use).
I hope that covers the so called "OS Wars", which don't really exist, except in the minds of a few " Unenlightened Amiga Users" :-P
I should also mention "Am1thc0n" (R) (Edit:-name changed to protect Amiga.org), and Ill fated project. Basicly and Emulator which ran on top of an x86 CPU and made it look like a 68K. This allows AmigaOS 3.1 to run on a PC without realising it is a PC (it makes AmigaOS think it's running on an Amiga without the Custom Harware)... A realy nice idea, though not as fast as a native OS. This was Poject was "killed" by the small mindedness of some of the parties involved.
The original author may or may not release a new project called Umilator which is a very similar idea, but with improvments.
This project is very similar to UAE, but faster, without the custom hardware emulation and is a comercial project.
I must appologise for any bias in this document as I am involved with one of the projects, but I have tried to be as objective as possible.