For anyone new to the thread be sure to go through these steps to address the battery issues after updating to iOS 5.0.1 or 5.1:
1. Reset all settings (settings app-> general-> reset)
2 a. Go through initial setup steps (lang, wifi, siri, enable location, etc) and choose setup as new phone (don't worry your apps, data, contacts, mail will still be there). Do NOT restore from iCloud or iTunes (It can copy back corrupt settings)
2 b. If you do not get the complete new setup screen with language setup and setup as new phone or restore from iTune/iCloud backup, be sure to go back to #1 and reset all settings again (it should happen the second time)
3. Turn off system location services timezone and iAd (settings -> location services -> system services)
4. Fully discharge battery (until you get the spinning wheel and it shuts off)
5. Fully recharge battery (overnight if possible)
In my experience this improves the Standby battery drain issue significantly in most cases. It reduces drain from 2-4% or more per hr to 0.5% or less. It has worked for many, many users now. If it does not work after a few try's you may have a real battery or hardware issue and should contact Apple. Good Luck!