Many times, few of which made much sense.
One time, I was dreaming that I was playing Pearl. I was on that route just south of Veilstone, and found a Shiny Shinx in the grass. Not thinking anything weird about this, I caught the Shinx. And then, I went right into another battle, without even getting to move anywhere. This time I encountered an Ariados (not Shiny), but its animation was different and it had Huntail's cry. I must have woke up right after that.
Another time, I was dreaming I was playing Red. I was in Pallet Town, and near the southwest corner of town, there was a gap in the fence, allowing me access to the tall grass. Yes, that tall grass, the stuff of legends and rumors. Naturally, I hauled ass over there. As soon as I walked through the gap, the graphics and music started glitching, but the game didn't freeze, so I walked around in the grass. I encountered a wild Clefable, at which point the glitching intensified (the music and cries were still legible, though). I sent out a Fearow and selected an attack, but the Clefable went first and used Roar, which instead of ending the battle, did damage to Fearow. That's all I can remember of that dream. And in my actual Red Version, the first two Pokémon in my party at that time were, you guessed it, Clefable and Fearow. The Clefable didn't know Roar, of course, though.
Another time, I dreamed I was in my house, in real life, and I spot a Shiny Slugma slithering around my brother's bedroom, melting every piece of furniture it touched. I try to grab it, but can't get close enough due to the heat. So I somehow pull a Poké Ball out of nowhere, throw it at the Slugma... and wake up. >_<
Now this one's where it just gets downright freaky. I had another dream one time, but I can't remember the details of it. All I know is that it took place around Christmastime, and that there was a Drowzee in said dream. What makes this freaky is Drowzee's Gold Version dex entry; "If you think that you had a good dream, but you can't remember it, a Drowzee has probably eaten it."