What is the benefit of using non-blocking sockets with the "select" function?

There might be cases when a socket is reported as ready but by the time you get to check it, it changes its state.

One of the good examples is accepting connections. When a new connection arrives, a listening socket is reported as ready for read. By the time you get to call accept, the connection might be closed by the other side before ever sending anything and before we called accept. Of course, the handling of this case is OS-dependent, but it's possible that accept will simply block until a new connection is established, which will cause our application to wait for indefinite amount of time preventing processing of other sockets. If your listening socket is in a non-blocking mode, this won't happen and you'll get EWOULDBLOCK or some other error, but accept will not block anyway.

Some kernels used to have (I hope it's fixed now) an interesting bug with UDP and select. When a datagram arrives select wakes up with the socket with datagram being marked as ready for read. The datagram checksum validation is postponed until a user code calls recvfrom (or some other API capable of receiving UDP datagrams). When the code calls recvfrom and the validating code detects a checksum mismatch, a datagram is simply dropped and recvfrom ends up being blocked until a next datagram arrives. One of the patches fixing this problem (along with the problem description) can be found here.

Other than the kernel bugs mentioned by others, a different reason for choosing non-blocking sockets, even with a polling loop, is that it allows for greater performance with fast-arriving data. Think what happens when a blocking socket is marked as "readable". You have no idea how much data has arrived, so you can safely read it only once. Then you have to get back to the event loop to have your poller check whether the socket is still readable. This means that for every single read from or write to the socket you have to do at least two system calls: the select to tell you it's safe to read, and the reading/writing call itself.

With non-blocking sockets you can skip the unnecessary calls to select after the first one. When a socket is flagged as readable by select, you have the option of reading from it as long as it returns data, which allows faster processing of quick bursts of data.

One of the benefits, is that it will catch any programming errors you make, because if you try to read a socket that would normally block you, you'll get EWOULDBLOCK instead. For objects other than sockets, the exact api behaviour may change, see http://www.scottklement.com/rpg/socktut/nonblocking.html.