Question: Which will run faster: four 1GB sticks of DDR2 RAM, or two 2GB sticks? Will they run at the same speed? I'm just curious since they are sold in both sizes, and I have four slots, but only two sticks currently. I would imagine the 2GB sticks would be faster, but I can see how the 1GB sticks could as well.

Answer: 
In short no number of sticks greater than the total number of memory channels will cause speed changes. If you have 2 1GB now you can pair them on one channel and add either 2 1GB or 1 2GB whichever is cheaper to the second channel and get the same results. Just remember to reference your motherboard manual and check if the slots are paired 1+2 then 3+4 or odds and evens. Then you will know which slot to move on of the existing chips into if you decide to add a single 2GB. Matching size for the two channels is always optimal for performance.
The main factor is the number of memory channels, and that you at least have as many RAM sticks as you have memory channels. This is usually two channels, but Intel's high end platform came with three channels.

Assuming you have two channels, and most everybody do, having at least two sticks is important. Going from two to four has a much smaller effect, but there is one. Bumping it up to four sticks means you (well, the BIOS does it for you) have to loosen the timings a little bit. The main one that affects performance is Command Rate, which you may be, with good RAM, be able to keep at 1T with only two sticks but you'll have to bump up to 2T with four. So in that sense 2x2GB is preferable to 4x1GB. But the performance difference is minor and you are unlikely to notice it. 

There is one other countervailing factor though. Higher density RAM is usually slower than lower density RAM. You can still get just as fast 2GB modules as you can get 1GB modules but you have to be willing to pay a little more. Even so, the performance difference would be so small that it is unnoticeable in all but the most bandwidth sensitive tasks. 

TL;DR: Two versus four sticks won't make any real performance difference. With only two sticks you will have an easier time to add more RAM if you want to at a later date.