What is a heavy, dense wood for a soundproof door assembly I am putting together?
I would do a hollow door like @Tester101 suggested, but instead of using Dynamat (which is expensive) I would use foam.

In high school, they would collect egg cartons so they could sound proof the audio rooms. You could use egg cartons as well or a cellular foam board.

Sound is produced by vibration. Thats why sub woofers aren't directional.

Using foam, the cellular structure breaks up the sound waves.

Wikipedia actually has a good write up on this.

Wikipedia Soundproofing

So, on the cheap - 1/8 inch or 1/4 inch plywood to make the door and inside, fill it with a not so dense (ie: a foam where you can see the cells) foam board.