How do I end an Open Borders agreement in Civ 5?

Unfortunately, it's not possible to cancel an Open Borders agreement. You just have to wait for whatever turns remain for it to expire.

Or you can go to war with them, which "kind of" cancels it :)

Agreements can't simply be canceled, that's why they're agreements for a certain number of turns. Think contracts. You have to decide if you're able and willing to handle the terms of the agreement (contract) before committing to it. If you break the agreement, it has serious retributions (or rather, you have to go to extreme lengths, war, and face the backlash to break an agreement). If that wasn't so there would be little point to most agreements.

"Yeah, let's do this defensive pact thing, unless of course you're being attacked, at which point I may simply decide to back out of the agreement..."

Update (2010/10/14): Apparently your problem is a bug and will be fixed.

http://forums.2kgames.com/forums/showthread.php?t=94438

• Diplomacy – Fix for never ending deals (peace, research agreements, etc).