[[UIApplication sharedApplication] sendAction:@selector(resignFirstResponder) to:nil from:nil forEvent:nil];
The responder chain is so under-used in iOS. I’ll definitely try to think of ways to solve problems using it in the future.
For those of you who haven’t coded for the Mac, nil-targeted actions are what makes menus (among many things) work. When you select “Copy” from the menu, this is sent to the first responder. If that happens to be a text field, that text field gets the chance to put things into the clipboard. If it had been a check box, the check box would have no idea how to copy. However, that check box might be in a window, which belongs to a NSDocumentController, and the document might have the concept of copying the document as a whole. The app would step through the responder chain for you, from the check box all the way to the document controller, and perform the copy. Magic!