Is there a simple way to compare apps in my iTunes library with those actually installed on my iPhone?
Two possible answers...

Assuming you've not actively deleted them from iTunes as well as from your iPhone...


Upgrade to iTunes 10.x if you haven't already
Plug your iPhone into your Mac, open iTunes, sync it.
Click on the iPhone in the side bar and go to the Apps tab


You'll see that some apps are checked and others are not. This is an indicator of whether or not they're installed on the device.

Pretty sure this got introduced in iTunes 10.x (hence the first step)

Assuming you don't delete your old emails... (e.g. Archive in GMail)

The iTunes store should have emailed you summaries of the apps you've purchased (even the free ones) shortly after their 'purchase', so, if you have an email account where you've kept those emails, you could search through them to get a list of each app you've purchased from the iTunes store.