I picked up a copy of the new Macintosh OS X, Leopard, and installed it last night on my PowerBook. It was rather more troublesome than I expected, and there are definitely a few rough edges. Here are the main points (including a strong warning).

• Obviously I prepared for this by doing a full backup. I wanted the backup to be bootable, in case my HD became unusable, so I carved out a partition on an external FireWire drive that was exactly the same size as my (80GB) internal disk. I used the Disk Utility “Restore” function to make an exact copy of my internal disk. One consequence of this was that the backup partition got the same name as the internal disk, “Macintosh HD”. This is probably significant – I had two mounted partitions with the same name.
• I started the upgrade by inserting the DVD and running the installer. What this does is to set the boot drive to the DVD, and then reboot. After rebooting, and accepting the license, the installation program asked me to pick the drive for the installation. It showed the partitions on my FireWire drive, but not my internal HD.
• What was going on? I checked with Disk Utility (available through the installer), but it couldn’t see any mountable partitions on my HD. I tried to eject the DVD, but I couldn’t. I rebooted off the (bootable) partition on the FireWire drive, but I still couldn’t see/mount my internal HD. I was, however, able to eject the DVD.
• Finally I decided to zap the PRAM in the PowerBook, by power-cycling and holding down Cmd-Opt-P-R. This allowed me to reboot the PowerBook from the internal HD. Check the disk… OK. Time to start over.
• I unplugged all external devices from my PowerBook, rebooted, inserted the DVD, ran the installer, allowed it to reboot, accepted the license, and was asked to pick from… no disks at all. My internal HD was still invisible. I ran Disk Utility, checked the logs, brought up a terminal, poked around, closed the terminal… and then, quite suddenly, my “Macintosh HD” appeared in the list. I have no idea what was going on. Was it checking the file system? If so, why was there no feedback… and what hadn’t it done the same with my FireWire drives?
• Relieved, I allowed the upgrade to run to completion. It took about 90 minutes.

So my advice: unplug all external devices before upgrading, and be prepared to wait for a while without feedback. (Others have reported similar issues on the Apple Support Forums.)
There have been a few other glitches. If you’re upgrading an existing Mail configuration, you should run Mail to allow it to update the mailstore, and then go through every preference option to make sure it’s configured correctly. Quite a few things have changed. I have been using the GPGMail plugin to manage gpg-encrypted email; the plugin no longer works, and Mail disables it.
I’m also having Wifi (Airport) problems. Every so often, I’ll see the icon grey out and I’ll lose the connection to my Airport Express; when I do, the system log contains messages of the form:

Oct 27 13:24:36 silk mDNSResponder[47]: Note: Frequent transitions for interface en1 (192.168.1.2); network traffic reduction measures in effect
Oct 27 13:24:36 silk mDNSResponder[47]: Note: Frequent transitions for interface en1 (FE80:0000:0000:0000:0211:24FF:FEA3:0C42); network traffic reduction measures in effect
Oct 27 13:24:36 silk mDNSResponder[47]: Note: Frequent transitions for interface en1 (192.168.1.2); network traffic reduction measures in effect
Oct 27 13:24:40 silk mDNSResponder[47]: Note: Frequent transitions for interface en1 (192.168.1.2); network traffic reduction measures in effect

This is probably a symptom of an Airport driver which is cycling the interface up and down inappropriately. I’ve also had /usr/lib/airportd crash with a SIGSEGV; I’m going to file the bug with Apple in just a minute. ((There’s an active thread over in the Apple forums on this topic. Looks like a major issue for a lot of people.))
One other oddity: the DVD includes a folder for “Optional Installs”. This includes the developer tools (as usual), but there is also an installer for a bunch of random stuff: obvious things, like various localization files, fonts, and printer drivers, but also various applications, some of which are part of the base OS. There’s no indication anywhere as to what you’re supposed to do with this stuff. ((OK, I take that back. Apparently you can choose not to install certain applications during the main installation, in which case you can add them later on. That makes some sort of sense – but I wouldn’t expect Safari to be on that list!)) I wound up installing everything except the unnecessary localizations and printer drivers.
Overall Leopard is very nice. The look and feel is much more consistent than before; Time Machine is gorgeous. Everything feels a bit more responsive, and Safari gives me far fewer “beachballs”. The controllable grid spacing in Finder is a great improvement. I haven’t tried Spaces yet, since I use multiple screens already.
More as I learn…
UPDATE: Apple has just released Login & Keychain Update 1.0 for Mac OS X 10.5 Leopard, which seems to fix the WiFi problem. Of course, in order to for you to be able to install it, your WiFi will have to stay up long enough for Software Update to download the fix…
UPDATE: Several comments here have useful links; in addition you might want to check out Eric’s blog.