You're looking for a bulk SMS provider that can send internationally. A web search for "bulk sms" will show tons, including some I have experience with: clickatel, mblox, clx. The simplest way to interact with such services is via HTTP by POSTing your submissions to their gateway.
I would suggest OpenMarket as a SMS aggregator. They offer Number Lookups as part of their service if you needed two-way communication with a Short Code.
If you just need to send a one-way SMS/Text message (Like alerts) but the user would have to opt-out via email and then be removed from your service. You could use something like
Neustar number verification LEAP to do a number lookup (Which displays the carrier information) and use the SMS Email Gateway to send the SMS messages.
We used them for a large-sized application to send alert notification messages and they were very reliable. They also give 15% discount for registered charities and academic institutions.
You might take a look at using a Google Voice API, because it'd be free.
I'm not sure which language you're using but here's a API for python that should let you do it.
http://code.google.com/p/pygooglevoice/
Try www.bulksms.com - they have been around for over 10 years now, and specialise in pure SMS messaging - nothing else. A simple HTTP API, good delivery, operational in UK, Europe, USA, Africa and more.
If you need verify an mobile number, not send sms and not confirm propietary, then you should search for "HLR Look up gateways", it´s cheaper than send SMS.