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...

1. Upgrade to iTunes 10.x if you haven't already
2. Plug your iPhone into your Mac, open iTunes, sync it.
3. 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.

drfrogsplat hit the nail on the head. Some other things of note are:

• If an App in is iTunes but not on your iPhone, you can delete it from there without ever having to bother your iPhone. As far as the iPhone is concerned, that app already doesn't exist.
• If an App is synced to your iPhone, if you delete it from either one when not connected for syncing, then it will be copied back across during the next sync. I've had a lot of apps "come back from the dead" in this fashion. If you want to delete apps that are synced the easiest way to be rid of them for good is to connect the iPhone to iTunes and then delete it from the App tab, then sync.