Not much to go on, but I'd say check to make sure your hard drive is no where close to full. Then startup off of the latest OS installer disk you have for it. Run Disk Utility to repair the startup drive and permissions. Remove anything plugged into you Mac while troubleshooting (printers, firewire drives, etc). Restart and try again.
If not, try a "safe boot' by holding down the shift key right after you hear the startup chime (you can let go when the little gear icons starts spinning). After it boots try to update again.
If that doesn't work, boot from the installer disc again and try and archive and install of the OS. Be sure to choose the options to save your files, applications and networks settings. After the install, repair the permissions and drive again, then use the Apple software update to get you up to the latest versions. When its all done, repair the permissions and drive one last time.