I'm currently looking into developing some simple iPhone games in my spare time and I've been reading through the documentation on Apple's website. I have a large amount of experience with C++ and OpenGL but I have never touched Objective-C or OpenGL ES. From what I can tell, OpenGL ES is very similar to the desktop equivalent, and I don't see too many problems with picking it up. However, Objective-C seems quite different to other object orientated languages I have used before.

I did read that it is possible to use C++ code alongside Objective-C. I am guessing it would be possible to write the main bulk of code in C++ and then use Objective-C/Cocoa libraries to interface with the hardware. Would this be a recommended approach, or would it be more beneficial for me to write the entire app in Objective-C? What methods are other iPhone game developers using?

Have you tried searching the forums? There must be at least ten topics on this

Yes, definitely search the forums, but use Google, using the site command, like:

iphone language site:idevgames.com

because the forum search here stinks.

Outside of that, I'd say that if you have a lot of experience with C++ and OpenGL, you might find looking at the oolong engine very helpful. Basically, yes, you can use like 90% C++ if you want to and only use Obj-C for OS interactions.