Upgrading drupal between major releases can be a bit of a problem as I found out when upgrading from v5.5 to v6. However, upgrading point releases can be relatively easy. Note that to keep the URL constant and place drupal in its own file directory I use a symbolic link. Depending on your web server you might need to set your configuration to handle that.
The strategy I use is to:
And voila! the site was upgraded with all the old stuff still available in case there was a problem and I needed to revert quickly. Note that this will NOT work for upgrading between major revisions, only minor ones.