Assuming this is same as my iPod Touch:
On your iPhone:
1. Go to Settings > Store
( you should see the option of automatically download new Music, Apps, and Books)
2. uncheck Apps
---- ABOVE WILL KEEP APPS DOWNLOADED ON YOUR COMPUTER (OR OTHER DEVICES) FROM AUTOMATICALLY BEING ADDED TO YOUR iPHONE.-------
By the By...
If you don't want stuff purchased on your iPhone to also be automatically downloaded to your computer...
Do the following:
- Go to preferences
- Choose the "Store" Tab (Again you'll see "Automatic Downloads" - Read the explanation)
- Uncheck anything you don't want on your computer.
Just to make sure I understand you correctly: the apps are downloading / installing themselves while you're on wifi and plugged in. ( not while syncing itunes )
If that's the case, likely something IS behaving funky.
( but note I'm not running iOS 5 so there might be somewhere else you need to change things that I'm not aware of...)
You might try the following
1. You can try the old 'wake up the prefs' trick: basically you change, then rechange your settings. in your case check the boxes ) close settings (maybe even hard restart your iphone ) then uncheck them again
2. If that doesnt work you might try to Reset your phone (Settings > General > Reset) starting with the least destructive first . (naturally back up first)
Last resort, If you really dont want the apps for any current devices, you can delete from iTunes - then drag a copy from the trash as backup (YMMV It works on Mac OS 10.6x / iTunes 5) Of course that's not a longterm solution
Good luck if all else fails go thru Apple's 5 R's ( which eventually walks you thru a full install )
This will sound odd & could be overkill, but so many folks had odd issues after upgrading to iTunes 5 / iOS 5
it seems like something in temp memory / caching could be responsible ...
The following was posted here as a solution for the battery issues, but might turn out to be one of those fixes that clears a host of problems, If all else fails, give it a try