Question: Situation: The server calls accept(). The client sends a SYN to the server. The server gets the SYN, and then sends a SYN/ACK back to the client. However, the client now hangs up / dies, so it never sends an ACK back to the server.

What happens? Does accept() return as soon as it receives the SYN, or does block until the client's ACK is returned? If it blocks, does it eventually time-out?

Answer: 
If the client never sends an ACK, accept() will either block or return EAGAIN if the socket is marked non-blocking.
In the case there is a failure, say, a timeout because a handshake does not complete, it will return -1 and set errno. I believe, after looking at the man page, that it will set errno to ECONNABORTED.