I've used clickatell (www.clickatell.com) for sending msgs to Europe, US and AsiaPac destinations. Prices are cheap, depending on destination & quantity - there is an online calculator you can use to estimate costs. The API is simple (HTTP REST). They also support two-way, bulk and MMS messaging service, but I have not used these.
I have had trouble getting messages sent to some carriers in Malaysia, but their support team was responsive and this issue was resolved within about 10 days.
I also like the online reporting tools which provides graphs of messages sent / success rates etc over time.
