To turn off data roaming on your phone, go to:

iPhone:
Settings > General > Network > Data Roaming (ON/OFF)

BlackBerry (OS 6):
Options > Network and Connections > Mobile Network > Data Service While Roaming (ON/OFF)

BlackBerry (OS 5)
Options > Mobile Network > Data Service While Roaming (ON/OFF)

Android:
Settings > Wireless and Network > Mobile Networks > Data Roaming (ON/OFF)