I have a class that has a state (a simple enum) and that is accessed from two threads. For changing state I use a mutex (boost::mutex). Is it safe to check the state (e.g. compare state_ == ESTABLISHED) or do I have to use the mutex in this case too? In other words do I need the mutex when I just want to read a variable which could be concurrently written by another thread?
It depends.
The C++ language says nothing about threads or atomicity.
But on most modern CPU's, reading an integer is an atomic operation, which means that you will always read a consistent value, even without a mutex.
However, without a mutex, or some other form of synchronization, the compiler and CPU are free to reorder reads and writes, so anything more complex, anything involving accessing multiple variables, is still unsafe in the general case.
Assuming the writer thread updates some data, and then sets an integer flag to inform other threads that data is available, this could be reordered so the flag is set before updating the data. Unless you use a mutex or another form of memory barrier.
So if you want correct behavior, you don't need a mutex as such, and it's no problem if another thread writes to the variable while you're reading it. It'll be atomic unless you're working on a very unusual CPU. But you do need a memory barrier of some kind to prevent reordering in the compiler or CPU.