I am told that certain (mostly older) DSLRs can sync (i.e. successfully work with flash) at shutter speeds faster than 1/250 of a second.

Which makes / models can do this?

###Update

1. Thank you for all your answers. Fantastic. Keep them coming.
2. I am asking this because I want to be able to have more control of ambient light.
3. I don't really care how a camera manages to sync at a higher speed - just the effect. (Some people seem to think I am only asking about electronic shutters, but I'm not: high speed sync is a great answer, as is anything else, no matter how esoteric).