Look at how small the pixels are on your monitor in 1280x1024 resolution.
Then look at the huge pixels on your tv at 640x480.
The games will look fine, just a bit fuzzier and less detailed. They will still look next-gen, you just wont get all the xbox 360 has to offer without an hd set. Just wait it out and get one when you can afford one (I'm gonna just use a monitor, by the way).
Search the faqs in this forum for some help.