I haven't used a smartphone outside the US, though international use is a major factor I'm sticking with Cingular (runs on GSM) rather than switching to Verizon (CDMA). I have used a Motorola v180 (regular flip-phone) in Thailand with a SIM card I bought there...

Anyway, my current phone is a Nokia E62, the Cingular-locked, WiFi-less version of the Nokia E61. The Nokia E61 should be available unlocked and with quad-band GSM (so works anywhere with a SIM card); it also has WiFi; ~US$400? Runs on Symbian O/S.

My previous phone was the Sierra Voq, which is triband GSM (should work on most GSM networks, but check, e.g. on GSMworld.com). It runs Windows Mobile 2003, and is a decent/good phone. Unlocked for ~US$100 (no carrier picked it up, so Sierra discontinued production). There are two versions, one for North America (available at Amazon.com) and another for Europe (which is more common on eBay). It has a nice flip-QWERTY keyboard.

As the above examples show, an unlocked GSM phone is your best bet. I have written reviews for the v180, Voq and E62 on Amazon.com (I know, shameless plug, but better than repeating my comments here!)

Good luck,

p.s. In case you didn't know - triband or quadband refers to the frequencies at which the phone can operate, 850/900/1800/1900 MHz. See GSMworld.com for more information.