What is the best way to solve an Objective-C namespace collision?

Prefixing your classes with a unique prefix is fundamentally the only option but there are several ways to make this less onerous and ugly. There is a long discussion of options here. My favorite is the @compatibility_alias Objective-C compiler directive (described here). You can use @compatibility_alias to "rename" a class, allowing you to name your class using FQDN or some such prefix:

@interface COM_WHATEVER_ClassName : NSObject
@end

@compatibility_alias ClassName COM_WHATEVER_ClassName
// now ClassName is an alias for COM_WHATEVER_ClassName

@implementation ClassName //OK
//blah
@end

ClassName *myClass; //OK

As part of a complete strategy, you could prefix all your classes with a unique prefix such as the FQDN and then create a header with all the @compatibility_alias (I would imagine you could auto-generate said header).

The downside of prefixing like this is that you have to enter the true class name (e.g. COM_WHATEVER_ClassName above) in anything that needs the class name from a string besides the compiler. Notably, @compatibility_alias is a compiler directive, not a runtime function so NSClassFromString(ClassName) will fail (return nil)--you'll have to use NSClassFromString(COM_WHATERVER_ClassName). You can use ibtool via build phase to modify class names in an Interface Builder nib/xib so that you don't have to write the full COM_WHATEVER_... in Interface Builder.

Final caveat: because this is a compiler directive (and an obscure one at that), it may not be portable across compilers. In particular, I don't know if it works with the Clang frontend from the LLVM project, though it should work with LLVM-GCC (LLVM using the GCC frontend).

If you do not need to use classes from both frameworks at the same time, and you are targeting platforms which support NSBundle unloading (OS X 10.4 or later, no GNUStep support), and performance really isn't an issue for you, I believe that you could load one framework every time you need to use a class from it, and then unload it and load the other one when you need to use the other framework.

My initial idea was to use NSBundle to load one of the frameworks, then copy or rename the classes inside that framework, and then load the other framework. There are two problems with this. First, I couldn't find a function to copy the data pointed to rename or copy a class, and any other classes in that first framework which reference the renamed class would now reference the class from the other framework.

You wouldn't need to copy or rename a class if there were a way to copy the data pointed to by an IMP. You could create a new class and then copy over ivars, methods, properties and categories. Much more work, but it is possible. However, you would still have a problem with the other classes in the framework referencing the wrong class.

EDIT: The fundamental difference between the C and Objective-C runtimes is, as I understand it, when libraries are loaded, the functions in those libraries contain pointers to any symbols they reference, whereas in Objective-C, they contain string representations of the names of thsoe symbols. Thus, in your example, you can use dlsym to get the symbol's address in memory and attach it to another symbol. The other code in the library still works because you're not changing the address of the original symbol. Objective-C uses a lookup table to map class names to addresses, and it's a 1-1 mapping, so you can't have two classes with the same name. Thus, to load both classes, one of them must have their name changed. However, when other classes need to access one of the classes with that name, they will ask the lookup table for its address, and the lookup table will never return the address of the renamed class given the original class's name.

Several people have already shared some tricky and clever code that might help solve the problem. Some of the suggestions may work, but all of them are less than ideal, and some of them are downright nasty to implement. (Sometimes ugly hacks are unavoidable, but I try to avoid them whenever I can.) From a practical standpoint, here are my suggestions.

1. In any case, inform the developers of both frameworks of the conflict, and make it clear that their failure to avoid and/or deal with it is causing you real business problems, which could translate into lost business revenue if unresolved. Emphasize that while resolving existing conflicts on a per-class basis is a less intrusive fix, changing their prefix entirely (or using one if they're not currently, and shame on them!) is the best way to ensure that they won't see the same problem again.
2. If the naming conflicts are limited to a reasonably small set of classes, see if you can work around just those classes, especially if one of the conflicting classes isn't being used by your code, directly or indirectly. If so, see whether the vendor will provide a custom version of the framework that doesn't include the conflicting classes. If not, be frank about the fact that their inflexibility is reducing your ROI from using their framework. Don't feel bad about being pushy within reason — the customer is always right. ;-)
3. If one framework is more "dispensable", you might consider replacing it with another framework (or combination of code), either third-party or homebrew. (The latter is the undesirable worst-case, since it will certainly incur additional business costs, both for development and maintenance.) If you do, inform the vendor of that framework exactly why you decided to not use their framework.
4. If both frameworks are deemed equally indispensable to your application, explore ways to factor out usage of one of them to one or more separate processes, perhaps communicating via DO as Louis Gerbarg suggested. Depending on the degree of communication, this may not be as bad as you might expect. Several programs (including QuickTime, I believe) use this approach to provide more granular security provided by using Seatbelt sandbox profiles in Leopard, such that only a specific subset of your code is permitted to perform critical or sensitive operations. Performance will be a tradeoff, but may be your only option

I'm guessing that licensing fees, terms, and durations may prevent instant action on any of these points. Hopefully you'll be able to resolve the conflict as soon as possible. Good luck!

This is gross, but you could use distributed objects in order to keep one of the classes only in a subordinate programs address and RPC to it. That will get messy if you are passing a ton of stuff back and forth (and may not be possible if both class are directly manipulating views, etc).

There are other potential solutions, but a lot of them depend on the exact situation. In particular, are you using the modern or legacy runtimes, are you fat or single architecture, 32 or 64 bit, what OS releases are you targeting, are you dynamically linking, statically linking, or do you have a choice, and is it potentially okay to do something that might require maintenance for new software updates.

If you are really desperate, what you could do is:

1. Not link against one of the libraries directly
2. Implement an alternate version of the objc runtime routines that changes the name at load time (checkout the objc4 project, what exactly you need to do depends on a number of the questions I asked above, but it should be possible no matter what the answers are).
3. Use something like mach_override to inject your new implementation
4. Load the new library using normal methods, it will go through the patched linker routine and get its className changed

The above is going to be pretty labor intensive, and if you need to implement it against multiple archs and different runtime versions it will be very unpleasant, but it can definitely be made to work.

Have you considered using the runtime functions (/usr/include/objc/runtime.h) to clone one of the conflicting classes to a non-colliding class, and then loading the colliding class framework? (this would require the colliding frameworks to be loaded at different times to work.)

You can inspect the classes ivars, methods (with names and implementation addresses) and names with the runtime, and create your own as well dynamically to have the same ivar layout, methods names/implementation addresses, and only differ by name (to avoid the collision)