NESticle x.xxx - DOS - Coded by the incredible Bloodlust Software AKA Sardu, NESticle is one of the best and most compatible NES emulators in existence.
NESticle x.xxx - WIN - This is just like NESticle for DOS but also has netplay features!
fwNES 0.302 - DOS - Another cool NES emu that plays some games NESticle cannot. It has support for the most mappers ever seen in a NES emu, it even emulates 5 sound channels (even the DPCM channel!)
RockNES 0.981 - DOS - Another highly regarded NES emu that continues to be actively developed. Keep an eye on this one!
FCE Ultra 0.17 - DOS - NIce NEs emulator with a number of good features, one of which is Nintendo VS. Unisystem support!
LoopyNES 0.51 - DOS - An interesting NES emu that has the ability to play the old VS. series of arcade games based on NES hardware. It also runs good on older PCs, if you have one of those, use LoopyNES! A beta of a newer version is available here
NES4PC 0.35 Alpha 2 - WIN - A very good NES emulator, but it requires quite an hefty PC to go fullspeed. It has a scanlines based graphics engine, which will give you that "TV" feel when playing. The Zapper and paddle are also supported, time to play "Duck Hunt" ;)
WinNES 0.0.6 - WIN - This is a fairly new NES emu, which will run on a system with OR without DirectX. It's still pretty much beta software, so you will have to try it for yourself and see if it fits your needs :)
FC Fan 1.07 - WIN - This is a very good emulator, but since it is in Japanese, it may not appeal to all people. This is worth a check though, it DOES require DirectX however.
Ultee 0.1.3 - WIN - This is a new NES emu with support for quite a few mappers. It has joystick support and uses DirectX for the screen rendering. Just try it and see if it fits your needs :)
Prentendo 0.04 - WIN - Fairly new emulator, getting MUCH better with every release.
REW 0.9LC - Windows - REW is an Gameboy emulator by the author of Dboy, it also supports some NES games.
JNES 0.30a - Windows - JNES is an emulator that uses DirectX and is mainly written in assembly, it also plays NSF files. If you're looking for speed, check this emu! (homepage)