In 2010 JackKane wrote a post in Stack Overflow with a nice synopsis of history of digital art in games. Before I start showing links to the best Pixel Art tutorials I have found, I would like to quote him. Because it is very instrutive and because I completely agree that the old 2,5D art was nicer than the 3D art that came to succeed it.
In the old days, sprites were hand-drawn pixel by pixel. This works well for flat 2D games (side-scrollers, cartoon adventure games, Z-axis top-down, and such), particularly if they are in the 320x200 resolution. Some examples of gorgeous hand-drawn sprite games are the Sierra and Lucas Arts adventure games, Disney's jump&runs, Capcom's fighter games, the Tyrian/Raptor-style top-down scrollers, and the early RTS games (C&C, WC1). Some games, like Prince of Persia and Mortal Combat, used sprites from animated actors. That produced fluid motion, but looked 'flat'.
Between the mid-90s and the early-00s, character/item sprite-drawing was done by taking stills of 3D objects. Practically every 2D RTS game since around Age of Empires 1 did that. AFAIK Diablo, Baldur's Gate, Divine Divinity, and other such RPG games did the same. This is the reason those games came on so many CDs - they were chock-full of content. This approach looks great (not flat, but "2.5D") but takes a lot of hard-drive space. Also, whereas you could produce hand-drawn sprites in Paint, the 2.5D ones require 3Ds Max (or equivalent). One problem that arises with this approach is the combinatorial explosion in costume design (i.e. if you want animate a character in three different coats with three different hats and three different pairs of pants, you need 27 distinct animation). The solution to this, as seen in Diablo II and Baldur's Gate, is rag-dolling - you produce different sprites for every part of the body. This takes a lot of work. Blizzard made their own tools to produce their sprites, but I'm not sure there are sprite rag-dolling tools in the open.
More recently, most games are 3D. Many actually look worse than the old 2.5D ones, because a simple 3D model can animate well in sprites, but poorly in real-time 3D. The difference is that between a glamor shot of a celebrity, taken from a certain distance in certain lighting and then worked-over in photoshop, and the appearance of the same celebrity in real-life (which may not be as glamorous).
This interesting post in Gamasutra by Adam Saltsman in 2009 tells about Pixel Art from a professional point of view, answering the question "Why Pixel Art?". As an additional benefit, it shows very nice Pixel Art images!.
Retronator Magazine & Pixel Art Academy
Well, Retronator Magazine is not just a tutorial page but a digital magazine dedicated to Pixel Art with a lot of cool stuff inside. Including news, reviews, tutorials and the Pixel Art Academy.