The original GameBoy was slightly smaller than a typical brick. It used 4 AA batteries and came in the same color as the typical PC case of the day. It had a monochrome display, a built-in speaker, 4 buttons (A, B, select, start) and a directional pad.
The GameBoy Pocket was much like its predecessor, except it was slimmer, came in different colors, and (if I recall correctly) did not have the battery life of the original as it ran off of 2 AAA batteries.
The GameBoy Color added the long overdue upgrade to a color display, surpassing the Lynx, though its color depth was still inferior to the GameGear?. It used 2 AA batteries and also sported a nifty infrared communications port that was for the most part useless except for mystery gifting.
The GameBoy Advance marked the GameBoy's first complete overhaul. The unit now sported power greater than a SuperNintendo. Indeed, it even added two shoulder buttons, allowing developers to possibly port SuperNintendo games to the GBA if they dropped two buttons. The new link cable also allowed for up to four players to play together without an extra accessory.
The GameBoy Advance SP introduced a clamshell design with a much-needed built-in lighting solution and rechargeable lithium ion battery. It also removed the headphone port, so you'll have to buy an adapter to use headphones on an SP.
The GameBoy Micro is the third variation of the GameBoy Advance. It includes all the features of the SP, but in a package barely larger than an Advance cartridge. It also allows for changing the faceplate, for the fashion concious among you.