Let's see, I think I never had any normal dreams, I would consider all of them weird. Or most at least. Maybe you can use some of them.
Anyone remember the lemmings? In one game, I think it was Lemming 2: the Tribes you had about 100 different jobs you could let your lemmings perform to get them to their goal. In one of my dreams, I was with a few friends at a house we had been a few times before in the summer vacations, although not everyone gathered there had been there in reality. Now the weird part was, that there was a huge building (think storage depot) right next to that house, when in reality the house itself was surrounded by forest. Inside this building was only one large room that contained showers on the walls, like you would find in a waterpark. However, you could chose a shower and then be transformed into one of the Lemming Jobs, depending on which shower you used. I went back to the house to find everyone there had chosen the same, which was a different one that I went with. I went a couple of times back an forth, everytime the others had changed as well, but I was never able to match up to them. Finally I woke up.
Another dream, I had this one quite frequently for a while, always started out the same. I was just about to drift to sleep but was not quite there yet, when I was suddenly sitting on my bike, riding it along a path that was maybe 2 inches wide and falling down endlessly on either side. To both sides was nothing for miles, below me were thick clouds that almost looked like the floor. After a while the path was twisting more and more, and it became harder and harder to stay on track. Eventually I fall down, which took quite a while, but when I finally crash on the clouds, I kinda crash down on my bed as well.
In yet another dream I am wandering through a forest. After a while the trees change, because now there are some trees that grow swords. A few steps further a hovering sword suddenly appears in front of me and starts attacking me. I pick a sword from one of the nearby trees to defend myself. The attacking sword disappears after I hit it hard a few times, and I continue my journey. The forest ends in a huge city, huge skyscrapers to all sides. After a while one of them is hovering in front of me, like the sword did and starts attacking me again. I grab the nearest skyscraper to defend myself again, and I always wake up before the fight really begins.
I realise, I never thought about my dreams this much. Good Lord, I think I need therapy
anyway, I hope you can use some of this. And I would really be interested to know how you are going to use dreams in your game.