WPA can be used with different protocols. Using WPA-TKIP, there are alternative attacks than the common handshake-bruteforce, but those will not grant you access to the AP. These attacks focus on RC4 weaknesses (similar to WEP, but far less effective due to successful countermeasures).
I assume that you want to acces an AP. In this case, bruteforcing is the only possible way to crack WPA. You capture a handshake between client and accesspoint, and perform the challenge-response yourself with different passwords, until your result matches the one you captured.
This can be sped up by using rainbow-tables, although you will have to find a target using a popular SSID in order to have an existing rainbow table.
Thus, to protect against intruders, you should choose an uncommon SSID along with a fairly long and complex password.
And no, you can not attack WPS when WPS is disabled or not supported. There may be bugs preventing a user from disabling WPS, but i consider these APs WPS-enabled.