TinySID is a very small SID player. Current features include 99% 6510 CPU emulation and fat 6581 SID emulation including filters (which sound different to other players). It has nothing to do with other projects such as SIDPlay, and the 6510/6581 emulation is based on routines by Tammo Hinrichs that have been further developed.
UAE is a mostly complete software emulation of the hardware of the Commodore Amiga 500/1000/2000. A Commodore Amiga, for those who don't know, is a 16/32 bit computer system based on the Motorola 680x0 CPU and a few specially designed custom chips that provide very good graphics and sound capabilities. Its first incarnation, the A1000, appeared in 1985, followed by the highly successful A500 and A2000 models. But if you didn't know, you probably don't want an emulator.
VICE is a Versatile Commodore Emulator, i.e. a program that runs on a Unix, Win32, MS-DOS, Mac OS X, Amiga, or RiscOS machine and executes programs intended for the old 8-bit Commodore computers. The current version emulates the C64, C128, VIC20, Plus4, C64-DTV, all the PETmodels, and the CBM-II (aka C610).
Virtual X68000 is a virtual machine that emulates a Sharp X68000 and optionally its DOS API. It will eventually run application programs for X68000 without any proprietary software including ROM BIOS, but currently lacks many key functions and is still in early development phase. Virtual X68000 is written in C++, and uses templates to implement instruction handlers.