I use them for four reasons - trigger, unloading, wife, and aesthetics.
The single action trigger of your basic Smith or Colt revolver has a trigger that I haven't found on any semi-auto (except possibly my late lamented Sig-Neuhausen P-210). Some target autos come close, but they don't actually match the garden variety revolver's trigger.
Many folks don't like to leave a firearm loaded in the house after bringing it home. For a semi-auto with a cartridge in the chamber, that means ejecting from that chamber, each and every time - that means many, cartridges are subject to "setback," in which the bullet is forced down into the case. I prefer not to do this more than once unless the case has a cannelure, and that isn't very common these days. With a revolver, you just open the cylinder and drop the cases back into the speed loader.
My wife doesn't enjoy firearms or shooting as much as I do, and getting her to practice with a semi-auto is an uphill battle, so limp-wrist prevention and malfunction clearing is a non-starter. Those things don't usually happen with a revolver.
Finally, I can see lots of folks coming back to revolvers for various reasons - check the prices on Gunbroker. They certainly aren't as effective as semi-autos in self defense, so there must be other reasons. Maybe it's history, maybe it's blued steel, maybe it's all those practical reasons about not needing magazines, but for me it's a feeling of self-containment. It's all right there - nothing drops out of it, nothing ejects away from it, it's just there, all in one piece. Call it art, history, call it aesthetics, soul, or self-containment. It's all right there and it doesn't always have a practical reason.