What is the minimum hardware needed to run Xcode 4?
1GB of RAM will kill you: frankly, I can't imagine that it would meaningfully run. I'm currently using a 2009 MacBook (not Pro) with 4GB of RAM, and for the first two or three hours Xcode runs pretty well. 

After that, though, it gets slower and slower. On a pretty small project Xcode will be using multiple gigabytes of RAM with the OS swapping 2-3GB to disk. Before long I not only have to quit Xcode, I also have to restart the machine to get things back up to speed. (To head off potential commenters, no, it's not something else on my system, it's Xcode 4: no other piece of software, including Photoshop operating on a 20+ GB file, fails to clear up the swapping speed problem after quitting the app.)

I can safely say, both from my experience and from talking to others, that 2GB of RAM is the bare, bare minimum, and it's not going to be a good experience. I'll be replacing this system soon, but in the meantime I'm upgrading to 8GB because I'm losing too much time to only having 4.