You need to change the DPMS settings, which are controllable with xset. You can disable all DPMS with:
$ xset -dpms
And re-enable them with:
$ xset +dpms
You can also control how long before the monitor switches into each state (standby, suspend, and off; they're explained in this Wikipedia article) by passing 3 integers for the number of seconds before each state should be activated:
# Switch to standby after a minute, suspend after two minutes, and off after three minutes
$ xset dpms 60 120 180
Setting a time of 0 disables the state, so -dpms is equivalent to:
$ xset dpms 0 0 0