This satisfies part of what you asked for (focused on retro-style video game sprites): http://charas-project.net/ and specifically their charset editor.
It isn't a pixel editor; it's a (large!) library of user-contributed sprite elements, and a web UI for combining them into a finished spritesheet. You can pick one of the user-contributed body types, one of the faces, hair, clothing, and up to three items, and it shows you a real-time preview of the results and lets you download the finished image. Very quick to put something together, but tweakable if you e.g. want the shield to be semitransparent or something.
It isn't arbitrary resolution; all the charset elements are for 24x32 sprites. But you automatically get three "walking" animation frames for each of four facings. Very useful for quickly building a Final Fantasy (I through VI)-style sprite, especially if you're not a hardcore graphic designer.
Here's a sample I knocked together in a minute or two (the site isn't the fastest, though response times are pretty reasonable for a free site with no ads):
The site also lets you build face graphics (e.g. for dialogue displays) and in-battle graphics, and there are libraries of spritesheets that others have developed on their own.