I have read studies which say (any my own experience confirms) that of all the things that can break on a computer, the hard drive is the most likely. Consider having a second hard drive with you with a mirror image copy of your normal drive. If your hard drive dies on tour, just plug the other one in.
Use External Storage
It's not so easy on some laptops (like new Mac Book Pros) to change out the hard drive. Expecially when an array of small tiped tools are not available. Storing your sounds (for example) on high speed Firewire external disk makes it easier to recover.
Handle Connections with Care
Unlike a desktop computer where you can always buy network, usb or firewire expansion cards if the built-in ones fail, it's not always that simple with laptops. The new Mac Books for example don't even have standard PCMCIA slots and there are not many options for their "Express" card slot.
Treat these built-in ports with care. I have been onstage when a crash cymbal was hit hard and fell and hit a firewire cable sticking out of a laptop and the slot stopped working. It wook us minutes to get the set going again on the internal sound of the laptop instead and it sounded pretty crappy. Be gentle with built-in ports. Don't just yank USB cables to disconnect. Treat connections with care.
Use dedicated performance user account
Both Mac OSX and Windows have the capability to start certain applications automatically when you login. Although it's tempting to say that you should just remove all of these, it's not always practical if you have to use your laptop for things other than performance. If you can't dedicate a laptop just to live use, at least use a different user account which doesn't have any applications starting when it logs in.
Have drivers/installs Backup
Many people back up their songs and sounds, but don't backup the actual install files for applications or drivers. Especially in Windows, it's common for the OS to ask to re-install drivers when you insert a USB device for example. Have a backup copy of any essential drivers or application install files with you in case you have to reinstall. Even if your laptop dies on tour and you can use a loaner, do you really want to try and download a 1.3 gig installer for Ableton over a hotel connection in a remote country?
Bring customer care/support info
So you have a warranty of some sort. Great! Does your vendor require a customer number or serial number you cannot easily identify on the machine to get support? Do you know the tech support phone number? If you have a hardware or other problem on tour and need to call support, make sure you have any relevant contact and customer care numbers with you.
Don't Leave your Laptop back stage or leave after SoundCheck
Over 50% of of all privacy breaches occur from a lost or stolen laptop. The thing that makes laptops so nice is also the thing that makes them so easy and attractive to steal. Portability. Don't leave your laptop unattended back stage or anywhere in a venue.
Enable screen locking but not screensaver
Screensavers are fun to stare at sure but they can also be a royal pain when they kick in on stage during a performance. However, do set your screen to lock after a period of time longer than your typical set and manually lock your screen every time you'll be away from the machine.
I played a show once where the local opener erased all the lighting presets from my controller because they were upset they didn't have a long enough sound check. I shudder to think if I had an unlocked laptop there what they could have done to mess up my set. Do not trust that no one will mess with your laptop in a club. Sounds obvious but so many bands do it. Lock the screen.
Most people will recommend that you defrag often. This is especially true for musicians and video artists where you work with large files that move around and change frequently. Although the recommendation is more commonly associated with Windows (there is no default Defrag utility in OSX) many have written that it applies to both to some degree and 3rd party OSX degrag applications are available.
Disable indexing applications
Both Windows and Mac OSX have native capability to index certain volumes on your machine to faciliate easy searching of files. (Office 2007 does this) There are also popular 3rd party apps which do this such as "Google Desktop". These types of applications eat away at your disk I/O which kills real-tiem audio/video performance. Turn this crap off when you perform.