Apple lifted the restrictions on non-Objective C/C/C++ apps -- you just can't load code that isn't in the app bundle.
MonoTouch lets you use .NET languages -- C# is directly supported, but if you have Windows, you can make assemblies in any .NET language and use it.
There are rumors that Apple is going to support other languages directly -- I keep hearing ruby, but they are just rumors.
I think Lua is being used for game logic on a lot of apps.
EDIT (in 2018): Generally you can use any language that you can get to compile for iOS or even install language interpreters. The main thing you cannot do is load code from the Internet that wasn't in the app bundle.
People do this all of the time anyway (see React Native apps loading JavaScript from servers), but, technically, it's not allowed. The main thing that will get you attention from Apple if you make some kind of App Store that loads whole App-like things.
EDIT (in 2020): from @Pylot in comments: I know this is a long time ago, but now at least technically you can load code that isn’t embedded in the app, as you can write with JavaScript using the webview. Not staying your answer is wrong or anything, I definitely agree with you. but I was looking for something and found this post on the way. Figured if anyone sees this it might help them out.