I just recently found out how to get my iPhone to start doing a full backup again. After updating to version 3.1.3, it would start the backup process and would take forever in backup – I had to stop the backup, but it would sync.

Turns out the problem was a corrupt app. Apparently there is a bug that corrupts your apps if you download and install an app on the phone and then transfer it to iTunes. Also found out that if you have over 200 photos in your Photo Album or Camera Roll, that can also cause a slow backup – in this case sync your photos to iPhoto (Mac), or My Pictures on Windows. Then erase the one’s you don’t need on the phone.

Here are two ways to fix the corrupt app issue.
Note that unfortunately with both of these methods you’ll lose data stored in either all of your apps or just the corrupt one(s).
I haven’t found a better a way to solve this.

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Found my solution at:
http://digg.com/apple/iTunes_and_iPhone_Slow_Backup_Fix
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Make sure your iPhone is not plugged in.

The long way – depending on how may apps you have:
In iTunes go to the Preferences and turn of the automatically sync devices. This is found under the Devices tab.

Next, plug in your phone.

After it appears under the Device section on the left side of iTunes, control click (Mac) or right click (PC) and select Reset Warnings. This will allow you to disagree to letting the iTunes send info about your usage to Apple (one of the sources of a slow backup).

Next, on the right side, select Apps.
If you remember when your iPhone started to act up, you could start by deleting your most recent apps by unchecking them from the list of apps to be synced. After that, click the Sync button on the bottom right corner. If your iPhone sync’s properly and it does a full back up, then you’ve found out which app or apps is/are corrupted. Remove those from your library and reinstall them from the app store, it’ll look like you have to pay for them again, but iTunes will recognize that you’ve purchased them already and you’ll get them for free. If you don’t find the corrupt app(s) the first time around and you have plenty of patients, you could continue down this route. Otherwise…

…You could try this method.

Same as before, make sure your iPhone is unplugged.
iTunes > Preferences > Devices
Turn off automatically sync devices > OK

Plug in your iPhone
When it appears under Devices, control click (Mac) or right click (PC) and select Reset Warnings

Next, select Apps from the right side of the screen.
If there is a check mark next to Sync Apps, deselect it. iTunes will warn you that you about to erase your apps and all data contained in them. Go ahead and continue. Once you’ve dismissed the warning message, click the Sync button on the bottom right, iTunes will attempt to backup, you can skip this by pressing the ‘X’ in the display bar at the top of the iTunes window. iTunes should now sync and erase ALL apps on your phone.

Once this is done, eject your iPhone and do a hard reset — press and hold the sleep/wake button and the home key until the red slider bar appears. Turn of the phone and wait a minute, then power it back up. Once it’s on, you should see your normal homepage and only the corrupt apps left on it. Take note of those apps and then press and hold the home key until your icons start to wiggle, then erase the corrupt apps from the phone.

Next, in iTunes, erase those apps (or don’t select them when syncing back your apps).

After that, plug your iPhone back in and then control click (Mac) or right click (PC) and select Back Up

Your iPhone should now do a full back up. Once that’s done, you can start add apps back to the phone. I did at many as 5 at a time. As a side note, don’t put anything back you haven’t used in long time or have no plans of using again.

If any of these two work, once you’re done and your iPhone is backing up properly again, you can turn back on the automatically sync devices.