General Motors' automatic transmission fluids are the Dexron series. The original was just called "Dexron." Dexron II was designed to be an improvement over Dexron and can be used in any transmission that required Dexron. Dexron III (it replaced Dexron IIE) is formulated specifically for General Motors' electronic transmissions. There is a special formulation of Dexron III for Saturn transmissions. Dexron VI can be used in any transmission that requires Dexron II or III.
Chrysler's automatic transmission fluid designated "Chrysler 7176" is formulated for its front-wheel drive transmissions. There are a couple variants. The first is 7176D, and it is essentially an upgrade and can be substituted for 7176. However, 7176E is formulated specifically for use in Chrysler's four-speed automatic transmissions. Cars built in 2000 and 2001 use ATF+4. Any newer Chrysler vehicles need ATF+5.
Type F was the original Ford automatic transmission fluid. Type CJ and Type H are special fluids formulated for specific Ford transmissions. They are not interchangeable with any of the other Ford fluids (or each other). Mercon V is one of the newest Ford automatic transmission fluids as of 2010. It is the right fluid for most modern Ford products. Ford Torqshift transmissions, though, need Mercon SP fluid.
BMW LT7114l and LA2634 are specially designed for specific BMW transmissions. Honda ZL ATF is the way to go for most Honda automatic transmissions. Mitsubishi's need either SP-II or SP-III. Nissan manufactures a fluid called "J-Matic" for their vehicles. For Toyota there are several different fluids: T, T-III and T-IV. However, many vehicles made by Toyota (including Lexus) can use Ford's Type F automatic transmission fluid, too.
In addition to the fluids made and for the automobile manufacturers, there are synthetic aftermarket alternatives available. These are designed for different vehicles and the best way to know which one you need is to consult the labels. You should consult your warranty, though, too. It's possible that using a fluid other than the OEM one voids your warranty.