Ive actually thought of this and have only really come up with a few specific coasters, and a few types of coasters that would be interesting.
Maverick is the first one that springs to mind. That 1st drop freaked me out going forwards the first time, going about it entirely backwards would be phenomenal until those quick and snappy trasitions kicked in. Then you would be in some serious neck pain til the end of the ride.
Skyrush is really the second one mainly for its fast ascent, quick change into its drop and all that airtime and turns. I honestly think this would be the best one to ride backwards imo.
Legend as well as Boulder Dash tie for specific coasters simply because their layout is more unknown and is constantly turning and not sitting in one specified direction for any decent section of track. I disagree with Jarrett about Voyage because its esentially an Out-and-Back type layout with the turn arounds only really being the only place that would essentially mess with your mind. The reason I say this is because youd be able to watch the return track run and get a proper guesstimate as to where the turns would be. It would still be fun mind you, but would still be able to be somewhat predictable.
Now then, as for the general types of rides. The Hypers/Mega/Gigas immediately spring to mind for this. The long ascent upwards would end up feeling a lot longer than what it really is, and the drop would be made that much more intense because of it.
Another type that would greatly benefit from this would be a majority of launch coasters. As in, ones that dont really do much beyond the launch for the simple reason of them not possibly being the smoothest thing out there. As awesome as a backwards Rock'n'Rollercoaster might be, it would almost certainly be a seriously rough ride.
Thats it that I can think of really.