If you're using the most recent version of WordPress, there are two ways you can update your plugins by just clicking a button (OK, maybe a couple, but it's still really easy).
Under Dashboard in your WP admin, there will an Updates option. Click on that and you should see something like this:
Choose Select All and then click Update Plugins and the system will do it for you.
I would advise against updating plugins totally automatically (as in without clicking any buttons yourself). It's important to check out the change log on the plugin's page and also its compatability with whatever version of WP you're running. For example, if you're running 2.8 you might upgrade automatically without checking only to find out that the latest version of the plugin isn't backward compatible with your WP install and requires WP 3.0.1.
The other way to update your plugins is to go to the Plugins page in the admin, sort by Upgrade Available, check the plugins compatibility and change log, select Upgrade Automatically and then reactivate the plugin when the process is done upgrading the plugin.