On this page, there are links to several tutorials covering all manner of artwork, including sprite art. No guarantees on how long the links will last, but then, the beauty of using a wiki is that anyone can submit corrections to them. Hopefully, this should provide a very good base of knowledge to work from. None of these can substitute for practice, rather these exist to guide your practice, and help it to improve your skill rapidly, rather than having you flog away at simple cartoon forms for years and not learn anything.
As stated in some of Jetryl's other tutorials here, do not jump into the sprite tutorials and ignore the works on general or figure drawing. If you intend to draw sprites well, the ability to draw and visualize the subject in a general sense is an absolute prerequisite. Without exception, the best sprite artists are such because they have good basic art skills; understanding of shading, light, proportion, edging, foreshortening, etc.
You can't fake those - even if you never practice anything but spritework, the tutorials for "higher art" are very applicable, and will improve your spriting skill considerably.
General Art Instruction
Andrew Loomis is a master of his field. READ THESE BOOKS. They are classics, and not only are of pristine educational calibre, but have also passed into the public domain, and can be downloaded for free. People willingly pay in excess of $100 dollars to get their hands on real-world copies of these now-out-of-print books, and if you have any interest in drawing human beings, they will help you more than the rest of the tutorials on this page, combined.
Itchy Animation has, amongst other things, a tutorial on the rarely-covered subject of the behaviour of light and its effects on color (rarely covered from an artists' perspective, that is).
GFXartist.com has several tutorials from different artists, including the painter Craig Mullins, who has, for nearly a decade, been the favorite artist of wesnoth's art slave "Jetryl," and has a good chance of keeping that position for the rest of either fellow's time on this earth. (J- I can't say enough good things about that guy; I would honestly rank him among the greats, like Rembrandt, or Picasso - he's *that* good. The tutorials posted on that site do him little justice - for a better sample, his personal site is http://www.goodbrush.com/ , which has over a thousand of his works.)
Itch Studios - no relation to the above link, has a good general tutorial on methods in art, including choices of color and lighting.
The excellent pencil artist Mike Sibley has a series of tutorials on techniques he uses on his site. Though some are a bit specific to drawing with graphite, his discussion of negative drawing is very useful to any artist.
Tutorials on using Computer Graphics Software
Good-tutorials.com has over 8000 various tutorials covering different aspects of the popular program, "Adobe Photoshop."
Cell-shading/Comic Art Styles
Michael Derenge does a color webcomic on keenspace called Pointless; He did a "how-the-comic-is-done" in his forums, going over the process he uses to create his comic, which uses a cell-shaded style.
The Polycarbon site has been around for a number of years. Patrick Shettlesworth has posted up several basic drawing tutorials, along with tips on computer techniques which can be used to really spice up art in a photoshop-like program.
Pens and Pixels has several very good tutorials on advanced cell-shading and coloring techniques.
Though focused in parts on the mechanics of running a webcomic, and the rather contrived "art lifestyle" that such people try to act out, this site does contain a number of good, basic tutorials on cell-shading.
Joe Brudlos has put up a few tutorials for the process he uses in creating pages in his webcomic, "Alpha Shade". There's a CG Photoshop cloud tutorial, Two flash tutorials and well as a 3 part explosion in Photoshop tutorial.
Julie Dillon has a few of her tutorials up on the "How to draw Manga" site. Though obviously focused on the style favored by Japanese comic artists and animators, it does cover all the basics of cell-shading rather well.
Dan Kim website Clone Manga has at least four comics in the works, currently, most in rather atypical (and thus, refreshing) styles. He has posted two drawing and coloring tutorials, for use in a photoshop-like program.
Though not so terribly informative, this tutorial is being linked based on the vast amount of time which the game "Oni" stole from Jetryl's teenage years.
With a name like SpriteArt.com, this site actually manages not to disappoint. Tutorials from several artists are present, as well as a good deal of gorgeous pixel art.
Zoggles has a wealth of tutorials made by many different people, some good, some bad.
A russian site featuring several tutorials - you may need to click on the "English" link to view the site in a language you can understand, unless you have the privilege of knowing Russian.
The following is a forum post on some spriting forum containing a list of links to different pixel tutorials. Some are of banal quality, your mileage may vary.
A rather large Japanese tutorial on spritework. Note that the tutorial is only in Japanese, and that the html does not automatically set the page to the Shift-JIS text encoding, which is necessary in order to view the page. Even if you don't understand the text, following along with the pictures may be more than enough to teach you something. There are several pages to the tutorial, the arrow links to switch between are at the bottom and top.