You can get LED bulbs for regular fixtures, which are very much dimmable -- check the individual bulbs, as you'll pay a bit more for the dimmable ones. (I suspect that there are also dimmable LED fixtures, but I have no direct experience with those.)

I have Phillips Sparkle Effect LEDs in my chandelier (just swapped out the previous incandescent bulbs) and I love them. Like Ellsworth-Hallett said, the color temp doesn't warm up like incandescent do when dimmed low, but it doesn't bother me at all. http://www.amazon.com/Philips-435057-Equivalent-Candelabra-Decorative/dp/B00LP9PYVA

I've attached a photo I took of LEDs dimmed low and an incandescent (foreground) dimmed low.

You can certainly get dimmable LEDs