"Hard water," that bane of so many existences, contains excess minerals that stick around after the water has washed away. Those minerals can leave a caked-on mess in pipes and on water faucets, streaks in toilet bowls and "hard-water spots" on shower doors that are impossible to hide and seem impossible to remove.
They're not, though. Vinegar will take care of those stains, too, but in this case try a diluted mixture -- half vinegar and half water. Wipe it on just like you would for the soap scum, leave it on for several minutes, and then rinse. For water spots on the metal rim, a citrus oil (like lemon or orange) can work wonders.
And once you've cleared the spots, consider applying car wax to the shower doors. It will seal the surface so it's harder for the minerals to deposit there (and easier to remove if they do). Just make sure you don't wax the shower floor -- you'll slip.
Once you've cleaned your shower doors of water spots, mildew or soap scum, the trick is to keep them that way. If you wipe the doors with a towel, keep them open for air flow, and spray on a shower cleaner after each shower, you'll find your weekly scrub-down to be a lot less time-consuming.
For more information on cleaning bathrooms (and everywhere else), look over the links on the next page.