Stiff/Straight-Legged DeadliftWith this version, you keep the legs more or less entirely straight and make more use of the lower back. People often stand on a platform to get a greater stretch on the hamstrings.
I like that this guy does a standard deadlift for the first rep. This is a good approach, since it can be disproportionately hard to do that first rep with this variation - making it hard to have good form on the first rep if you are using a heavy weight. Another approach, if you have the necessary equipment, is to take the weight off a rack at waist height to start.
Romanian DeadliftSome people seem to think the Romanian deadlift is basically the same as the stiff-legged. But there are some differences and this article explains them well. Essentially, you do not go as far down with the bar (i.e. do not stand on a platform) and therefore there is no rounding of the back at the bottom. You also bend the legs a little more.
23.09.10: I recently videoed myself doing RDLs, and found my form was not good. After dropping the weight, and trying again the week after, things are looking better: