I find having to have an administrator password quite annoying, since I'll be the only one having access to my computer.
The main benefit of having an admin password is that you have to authorise any activity which modifies parts of the system outside your personal settings and files.
In theory this means that you are much less likely to unwittingly install a virus or other malware on your system. Some distros (eg. Ubuntu) have a more convenient method whereby certain users are given "sudo" priviledges. This means that they can use their normal login password to perform tasks that affect the whole system (instead of having a separate user ID / password for these activities)