If you mean literal Nightmares, as in going to bed and having scary dreams.....well that only happend once as far as I can remember, and from something I wasn't even scared of when watching that story. It was the Dalek...in well Dalek
The episode hadn't scared me or anything, but I remember having the dream, either on the same night or a few days later, where the Dalek was chasing me, and I made the stupid decision of running upstairs....so you can probably guess what happend in the end!

So yes strangely enough, and episode that I enjoyed very much so, didn't scare, gave me nightmares!!!
If we talk about the fear while watching the stories, the fun scares, well then it hasn't happend that often, but The empty Child appearing in its room after the tape ran out, the end of Blink, with the normal statues, the scarecrows in FOB, Toby in the Satan two parter, the man turning into the warewolf in Tooth and Claw.
The scares that actually sent a proper chill down my back have been, most of Midnight!, The end of Waters of Mars, the holocaust/labour camp references in both POTO and Turn Left, the scene where the Daleks kill the whole family in Stolen Earth, the end of Family of Blood, and the Cabinet scene with the Master.