Two ball tricks, um, there's one I like which involves a bit of illusion, so to speak. The key part of it involves 'sucking' one ball from one hand to the other. For example, take a ball in your left hand (facing up), and position your right hand above it. Draw your right hand upwards, while gently throwing the ball up from your left hand, so as to make it appear that your right hand is drawing it upwards. You should catch the ball at about the peak of its arc, and keep the right hand moving a little after you've caught it to help maintain the illusion.
Now with two balls, one in each hand, you can do the same thing; first throw the right ball in a gentle small arc to the left, and then do the trick described above, and catch the first ball in your left hand after you've thrown the second. Repeat :-)
Alternatively, you can alternate between drawing up the right hand and the left.
Another one, which is along the same lines, is to hold a ball in your hand, facing down (like a claw), at about waist level. Bring it up rapidly, and extend ones hand out flat, so that it appears that the ball is stuck to your palm. Once it starts to fall away, follow it down with your hand so that it still looks stuck, and catch it at the bottom and repeat. This looks neat when done with both hands, left then right then left, etc.
I've seen people do parallel contact juggling tricks with two balls, but I lack the skill to perform or describe them :)
A neat two ball trick that I've always liked uses the same basic move [as described by Sam Yates above]. This trick also gives the illusion that one of the balls is moving upwards on its own. Start by holding one ball in each hand, one facing downward and the other facing upward. The hand holding the downward facing ball should be about shoulder height and the other should be above the waist. Now drop the higher ball at the same time you throw the low one up. The throw should peak at the shoulders. While the balls are in the air, the hands should move laterally to catch the balls thrown from the opposite hand. Try to make the balls move on the edge of a square plane in front of you. After catching the balls, move your hands laterally again back to the starting position and repeat. You can get an interesting robotic looking move out of this where the balls move in a square in front of you. When done properly, the upward thrown ball seems to move up by itself.
Another move is what I would consider a 'classic' since it seems to me that I've seen it done ever since I started juggling. Hold one ball in your hand facing down at the floor. Hold it with your thumb and two smaller fingers so that the index and middle fingers are free. Now make a peace sign with these fingers and balance the other ball in the groove so that you are now holding both balls with the same hand. Now move the hand upward, releasing the ball being held. Grasp the ball that was being balanced, quickly reform your hand to its original shape and catch the released ball. In short, make the balls trade places. This can be done in a daring and impressive way such that an audience might OOOH or AAAH for you. Make the catch as close to the floor as possible to make it look difficult.
Much more simple than than tricks described so far, is a 3-ball cascade with a gap (330 ?). Then if you use the gap to wave to the audience (or mop your brow) you will find that people find it looks quite impressive. This can be used quite nicely as an introduction to the 3-ball cascade, and is just about as easy with clubs as it is with balls.
My favorite two-ball tricks are 40303, 411, and the amazing 501, a two-ball pattern that can actually help you learn 5! [see the siteswaps files -mpg]
There's a silly two ball trick which someone showed me as a way of learning a "proper" three ball trick.
You hold one ball in each hand, palms down (claw style), with your arms crossed (say left arm over right). Then which ever hand is underneath (right hand) throws the ball strait up and catches it over the other arm. Now the arms are crossed the other way (right arm over left) and you just repeat the trick with the other hand etc.
The balls never change hands, but when the trick is done fast and fluently it's quite difficult to work out what's going on.