I was able to teach my dog tricks pretty easily, with some patience. She learned the following:
-"stand" (sit down and lift up her front paws)
-"jump" (stand on her hind paws)
-"paw-five" or "give your paw" (including pawing a moving soccer ball passed to her, though that took some extra training) and
-"roll-over" (though I have to get her to lie down first, and it was difficult to teach her due to her large size... it's easier for smaller dogs).
My cousin's dog does that incessantly, asking for petting.
Unfortunately he also pees all over the place whenever anyone visits the family's house. They put him in the garage when I was there for supper, and I went to say hello to him in there. As he whined he sprayed a figure eight around the whole garage. I couldn't help but laugh as I tried to appease him with petting, hoping he wouldn't start again.
A family friend's old dog would sing along to the piano.
Pink Floyd also recorded a concert at Pompeii with their unofficial mascot dog singing along (now on DVD). If I could find a video of that on Youtube, I would post it. It was really funny.