Are there any special types out there or are they pretty much all the same?
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The two most common sizes are 3/32" and 1/8" Generally you would use 3/32" for bicycles which have dérailleur gears (road/mountain bikes). As for length I believe they are all a stock length and you'll be very unlucky if you find it is too short. You will need to specify how many speeds your freewheel or cassette is (6/7/8/9/10 speed).
You will obviously find lots of variety in quality/weight/material/price etc when you know which type of chain to look at.
The last major change in chains happened around 1990, when Shimano changed to their HyperGlide technology. The goal of HyperGlide was to offer more sprockets but retain the same overall axle width for the rear wheel.
Since then, anything with 8 or more gears in the rear cluster has used the narrower chain.
There have been recent developments around asymmetric chains, where the plates on one side of the chain are different from the other side (which makes it possible to install a chain "backwards").
For most vanilla applications, there isn't a gigantic difference between the narrow Bell chain at WalMart and the SRAM chain at your LBS.