I just acquired a Sony VAIO SZ680 and I felt like sharing my experience getting Debian installed on this thing. I wouldn't call it a “walk in the park” by any means, so hopefully someone else will find this useful.
Read it in this blog
Enough about that, lets first start with what DID NOT work:
Ubuntu 7.10 (gutsy gibbon)
Debian Etch (official release)
Ubuntu will eventually support this laptop, and you may be able to get it to work, but not without some effort. The primary problem is that the kernel installed by Gutsy hangs during boot just after is initializes the USB subsystem. I may end up debugging this issue on my own at some point, but right now I'm interested in just getting something to work.