JiveTurkey

Shimano Rear Derailleur Compatibility Chart:

Road SS ("short" cage)............Double chainring....27T or smaller cassette
Road GS ("medium"/"long").....Triple chainring.......27T or smaller cassette
MTB GS ("short"/"medium").....Double chainring.....28T or larger cassette
MTB SGS ("long" cage)............Triple chainring........28T or larger cassette

Models are "upwardly" compatible (that is, a given model will also work with the setups listed above it).

The chart is just a quick, general reference, but be mindful of and don't exceed the "Total Capacity"* of the RD. For example, 50/34T compact cranks have a larger tooth difference than 53/39T and 50/36T, so a Road GS model may be necessary if you're using anything wider than a 12-25T road cassette.

Be aware that most MTB RDs have a 34T largest cog limit, but some smaller, like 30T (Shimano Alivio).

*Capacity (in teeth) = [(largest chainring + largest cog) - (smallest chainring + smallest cog)]
E.g.: The Total Capacity of a Shimano road SS RD is 29T >= [(53+27) - (39+12)], or [(50+27) - (36+12)], or [(50+25) - (34+12)], or [(50+25) - (34+12), etc.]

Edit: In the chart above, Single chainring can be substituted for Double chainring.

Edit2: The large-cog capacity of a road RD can often be exceeded with ease (but may lead to the RD bumping into the cog in the lowest gear--often with a triple crank). Also, the chain wrap capacity can be exceeded, but it will render some gear combinations unusable (the small chainring ans smaller cog combos, which shouldn't be used anyway).