App Store is stuck in a loop trying to download a free app -- how do I make it stop?
Apple's servers were very overloaded with the iPhone 6 preorders.


http://www.apple.com/support/systemstatus/


The official system status page for Apple shows that things have cleared up, so most people with problems installing or downloading things can reboot their devices and then try again to get proper download and purchase behavior.

Expect some slowness this next Wednesday the 17th through Friday the 19th of September with iOS 8 coming out and iPhone 6 being delivered and activated. iCloud backups and restores should be slower than normal as well as possible store and purchase / AppleID slowness if the authentication servers come under large strain again.

In the short term, you could pause the download or turn off your networking and then sign out of the store. At that point, rebooting and trying again - waiting longer between attempts is a good first attempt. Also, Apple does support users on store download issues - so if you've waited several hours/days, contacting store support might be a next step.