I'm not one of those really great spriters, but I've been told that I've done a few decent sprites here and there. When newer editors are having trouble with something, I try to help instead of trying to score points by making fun of them. So here is where I'll put a few of my tips and methods.

Sprite Work:

Basics Clear, Resized Sprites on the Internet Sprite Bases Frankenspriting Sprite Ripping - Genecyst tricks

Other:

Lifebar Value Conversion

Here are some useful links to programs and to tutorials done by people who, unlike me, actually know what they're doing.

Other Tutorials
2D Will Never Die - Pro Tips	The tutorial index for Kiwi's amazing pixel art site.
Pixel Tutorial	"So You Want To Be A Pixel Artist?" by Tsugumo. Consider it a sprite bible. Talks about a wide variety of sprite-based topics including essential basics like RPG floor tiles.
Sprite Domain	Excellent tutorial about creating sprites from scratch
IRWT - Mugen Works	Orochi Gill's site has far more than just MUGEN downloads. You'll find articles that run the whole range of spriting tips and talk more about spriting concepts like style-specific color use than you'll find in most places. The "No, sir, I don't like it!" article is also a must-read for those who plan to work on characters or whole games.
Utilities
Zophar	All the emulation stuff that you need. Use the links to the right of the page to get to Zophar's areas. Get an emulator that has a "shots factory" mode that lets you turn off individual bg layers and sprite sections. For SNES, get ZSNES. For Genesis games, try Genecyst. For most fighting Capcom and SNK fighting games get either Kawaks, Nebula or SFMame.
	GraphicsGale: Graphics program with lots of bonus features for spriters. There's even a nice shareware version to try out.
emuhype	emuhype: Home to the Modeler emulator and the great M1 sound ripping program that allows you to get sounds from arcade roms. Try the version of M1 with the Fox frontend, too.
DOSBox Wiki	DOSBox: If you use an operating system (including Windows XP and Windows Vista) that won't allow you to run DOS programs properly, DOSBox will allow you to do it easily. I've linked to the Wiki so you can quickly look things up and it has a Downloads page to download it from.
BloodLust Nesticle and Genecyst	Bloodlust is behind two classic DOS emulators, Nesticle and Genecyst. While there are lots of fancier programs out there now that can run in Windows mode, these two programs make screenshots that allow you to easily rip sprites with 0/0/0 black in their palette as I do in the 'Genecyst tricks' tutorial.
ZSNES	ZSNES makes screenshots with true index palettes so that the 0/0/0 black in sprites and 0/0/0 black of background layers (even when turned off) will be separate. See the Genecyst tricks tutorial here for details.