First what u have to look before buying a mobile phone in other countries and also want to use them wherever you go is their Operating frequncies
Operating frequncies differ from country to country, example if you take U.S for instance their operating frequencies are entirely different from other part of the world its like "U.S and Rest of the World", there are two things involved here one is operating frequency of GSM and WDCDMA(for 3G)
Note: For detailed information look here GSM and WCDMA also look UMTS
Want to know what is the Network band for your country Look here
Now consider this case where your device is a Quad band GSM and triband WCDMA one which works on 850/900/1800/1900 GSM networks and 900/1900/2100 WCDMA networks and you have bought this device in India and want to use it in the U.S
For a mobile device to work in india it should support GSM 900 and WCDMA (for 3G) 2100 frequency bands atleast, on the other hand the same device to work in the U.S under GSM and WCDMA(for 3G) it should support GSM850 or GSM1900 and WCDMA 850 or 1900 frequency bands, now select a device which works on all these frequencies and you are good to go, its worth looking into the company website before buying the device, its not going to take any hard time to check whether it supports all frequencies that are out there considering you want to the device to function wherever you go
Some devices may not work on all 3G netwroks it depeds on the service provider you choose but a device of above specification works on all GSM networks
comments welcome.........