Depends on what platform you are using, and the command you are running.
For example, on Unix/Linux you can append > /dev/null & to the end of the command to tell the shell to release the process you have started and exec will return immediately. This doesn't work on Windows, but there is an alternative approach using the COM object (See edit below).
Many commands have a command line argument that can be passed so they release their association with the terminal and return immediately. Also, some commands will appear to hang because they have asked a question and are waiting for user input to tell them to continue (e.g. when running gzip and the target file already exists). In these cases, there is usually a command line argument that can be passed to tell the program how to handle this and not ask the question (in the gzip example you would pass -f).
EDIT
Here is the code to do what you want on Windows, as long as COM is available:
$commandToExec = 'somecommand.exe';
$wshShell = new COM("WScript.Shell");
$wshShell->Run($commandToExec, 0, FALSE);
Note that it is the third, FALSE parameter that tells WshShell to launch the program then return immediately (the second 0 parameter is defined as 'window style' and is probably meaningless here - you could pass any integer value). The WshShell object is documented here. This definitely works, I have used it before...
I have also edited above to reflect the fact that piping to /dev/null is also required in order to get & to work with exec() on *nix.
Also just added a bit more info about WshShell.