Google's API prohibits use without displaying a map and also no automated requests. While the Mapquest/Nominatim APIs are good, I want to add a note of caution.
International addresses are fairly easy to suggest to users -- if you don't care about accuracy. If you only want to suggest correct addresses, however, the task becomes much more complex. Each country's postal agency (e.g. the USPS, Canada Post, etc) handles their official records differently. Many countries don't handle them well, and even fewer provide ways for you to query their records.
For example, I work for SmartyStreets (US-based), where we do CASS-Certified US postal address verification. In the US, that means that suggestions we return are only correct addresses. Google, Yahoo, even MapQuest, perform address approximation, not address validation. In some cases, you will get results which are not valid, but you'd never know it.
Just food for thought. If you have any other address-related questions, just let me know; at least for US-based addresses, we can help you quite comprehensively.