Shimano has 2 types of rear derillauers: top normal and ..other type.
Which one works with STI? can you tell by looking?

Top or High normal is the "road" standard. A top normal MTB derailleur will work with a STI shifter. Be careful of some of the modern XT and XTR derailleurs which are low normal.
http://en.wikipedia.org/wiki/Derailleur_gears

How do you tell? If you are holding it in your hand - does the spring collapse it tightly to the smallest sprocket on the cassette like a road derailleur would?

Can you tell from a picture? Not that I know of, but someone else may know better.

most of the top normal derailures end in a 1 - ie 761, the low normal version would be 760. Supposedly the new shadow ones are top normal too.

low normal, rapid rise

whatever they call that poop

Cable pull is the same for either, so it comes down to personal preference which derailleur you choose. High normal is more common as the user generates the force to move the chain to a larger cog.