How to upgrade MySQL to newer version on existing database
Well, first off, if you are upgrading from 5.0 to 5.5, you really need to do this on a test server prior to making the upgrade in a production environment. This will get you comfortable with the steps of upgrading and let you figure out any trouble areas beforehand, which will dramatically reduce your downtime of upgrading.

So to upgrade, I would upgrade from 5.0 to 5.1, then 5.1 to 5.5 as the manual suggests. There will be downtime, but if you do the upgrade steps on a test setup first, you will reduce your downtime dramatically. Make sure you have all the installers downloaded beforehand, don't wait to download them while you're in downtime.

You could do the replication setup as Rolando points out, but please don't do the upgrade on production without testing out the steps first.