I'm going to go as far as saying that having to manually add error checking and propagation code to every function in your program is so bad (in several ways) as to be flat-out unacceptable. In my experience, the main kind of situation where it's okay to do without exceptions is when you can handle an error by printing an error message and promptly exiting the program. (Of course, this can be regarded as throwing a coarse-grained exception for which the operating system provides the handler and cleanup.)
Exceptions have the same problem as return codes in that you need to be careful to leave things in a consistent state if a function throws an error. RAII can help to some extent in both cases, but doesn't magically enforce that your classes and data structures are internally consistent.
My experience has been that error paths have a way of getting things into inconsistent states, and then you're in trouble regardless.
Checking return codes is annoying but if you're wanting to write robust software, your code needs to be in some way aware of every possible error path.
