Using your iPhone abroad is expensive, so to keep costs down make sure you have Data Roaming turned off:
Settings -> General -> Network -> Data Roaming
Furthermore, make sure that auto-checking of email is disabled:
Settings -> Mail -> Auto-Check
Finally, turn off visual voicemail before you travel:
Dial 1760 to switch the divert to voicemail off and dial 1750 to switch on the divert to voicemail.