If you get something like an eyeTV hybrid then you can connect in what they call 'gaming' mode, i.e. no lag. I have never tried it myself but people say it works well.
Unfortunately, at the moment there doesn't seem to be a way of getting HD out of your 360. I read somewhere that there's also some problems with games that require a higher frequency. Real shame, I would love to run a console on my iMac.