The strength and weakness of fork
(and company) is that they create a new process that's a clone of the existing process.
This is a weakness because, as you pointed out, creating a new process has a fair amount of overhead. It also means communication between the processes has to be done via some "approved" channel (pipes, sockets, files, shared-memory region, etc.)
This is a strength because it provides (much) greater isolation between the parent and the child. If, for example, a child process crashes, you can kill it and start another fairly easily. By contrast, if a child thread dies, killing it is problematic at best -- it's impossible to be certain what resources that thread held exclusively, so you can't clean up after it. Likewise, since all the threads in a process share a common address space, one thread that ran into a problem could overwrite data being used by all the other threads, so just killing that one thread wouldn't necessarily be enough to clean up the mess.
In other words, using threads is a little bit of a gamble. As long as your code is all clean, you can gain some efficiency by using multiple threads in a single process. Using multiple processes adds a bit of overhead, but can make your code quite a bit more robust, because it limits the damage a single problem can cause, and makes it much easy to shut down and replace a process if it does run into a major problem.
As far as concrete examples go, Apache might be a pretty good one. It will use multiple threads per process, but to limit the damage in case of problems (among other things), it limits the number of threads per process, and can/will spawn several separate processes running concurrently as well. On a decent server you might have, for example, 8 processes with 8 threads each. The large number of threads helps it service a large number of clients in a mostly I/O bound task, and breaking it up into processes means if a problem does arise, it doesn't suddenly become completely un-responsive, and can shut down and restart a process without losing a lot.