I upgraded from 1.3.9 to 1.6.6 without intermediate upgrades. So far, I've not noticed any problems.
I upgraded a copy ("WikiNew"), in order to safely test the process and not disturb the live wiki, so I had to copy the Images directory over from the live wiki. I also had to make a copy of the MySQL database and link to the copy. I had mods to the old Monobook skin, so I had to merge them into the new css code which is in a different directory now. And then I had to manually find and copy mods to the 1.3.9 code...
When I was comfortable, I renamed the root directories, and adjusted the LocalSettings.php file accordingly. This leaves me using a different database, with a different name. There were no edits on the old wiki during testing, otherwise I would have had to either upgrade the live wiki, or copy the edits across.
I don't think I had to run any maintenance scripts, I think all the upgrading of the database was performed in the main install script which is run the first time you access the wiki from a browser without the configurations established.
James