POSIX allows mutexes to be recursive. That means the same thread can lock the same mutex twice and won't deadlock. Of course it also needs to unlock it twice, otherwise no other thread can obtain the mutex. Not all systems supporting pthreads also support recursive mutexes, but if they want to be POSIX conform, they have to.
Other APIs (more high level APIs) also usually offer mutexes, often called Locks. Some systems/languages (e.g. Cocoa Objective-C) offer both, recursive and non recursive mutexes. Some languages also only offer one or the other one. E.g. in Java mutexes are always recursive (the same thread may twice "synchronize" on the same object). Depending on what other thread functionality they offer, not having recursive mutexes might be no problem, as they can easily be written yourself (I already implemented recursive mutexes myself on the basis of more simple mutex/condition operations).
What I don't really understand: What are non-recursive mutexes good for? Why would I want to have a thread deadlock if it locks the same mutex twice? Even high level languages that could avoid that (e.g. testing if this will deadlock and throwing an exception if it does) usually don't do that. They will let the thread deadlock instead.
Is this only for cases, where I accidentally lock it twice and only unlock it once and in case of a recursive mutex, it would be harder to find the problem, so instead I have it deadlock immediately to see where the incorrect lock appears? But couldn't I do the same with having a lock counter returned when unlocking and in a situation, where I'm sure I released the last lock and the counter is not zero, I can throw an exception or log the problem? Or is there any other, more useful use-case of non recursive mutexes that I fail to see? Or is it maybe just performance, as a non-recursive mutex can be slightly faster than a recursive one? However, I tested this and the difference is really not that big.