No. They don't repair them. They replace them.
Why would you not want a newer phone? Aside from the obvious improvements to the hardware, there is the issue that carriers are beginning to shut down their EDGE networks. If you're in the US, you will soon not even be able to use that phone as a phone at all.
Apple does not have an iPhone replacement service, but they do have display repair service. So you may arrange the display repair for $149,99, send them your iPhone, and they will send make a like for like change. You may receive:
-the best case - the new iPhone 2G, (of course not retail box, no charger or other accesories, you will receive just phone sealed in tape, in a small white box).
- the worst case - the new iPhone 3G, 3GS or 4 (the same no retail box, etc.).
If you are lucky, you will receive the iPhone 2G which is more than $500 worth on eBay.