I've read posts from folks who started at 10.1 and upgraded all the way to 10.8 without any issues.
That said, you can definitely chain update your way from 10.4 to 10.8 without issue, and similarly from 10.1 to 10.5. The latter case is a little tricky as many of the machines that ran 10.1 were not deemed fit for 10.5 (e.g. the G4 Cube variants), but there are workarounds.
I routinely have coped my bootdisk from Mac to Mac as I upgraded systems.
I should know this actually, I built OS X Live DVDs back in the day...