Disclaimer, I do developer evangelism part time at Nexmo.
If you're looking for an API to send SMS with a large global reach and high deliverability, you should check out Nexmo.
I don't recall the exact number, but for outgoing SMS over 200 countries/800 carriers (I think that's more like 1K now) are supported. It doesn't seem like you'll need incoming, but if you do, you can get inbound numbers in 14 (that number is also growing) countries.
As to reliability, I believe Nexmo is the only SMS provider that publishes delivery stats. I've pasted the delivery status for Israel here:
Network | Success Ratio | DLR Ratio
42503 Pelephone | 91.47 | 99.99
42502 Cellcom | 92.01 | 99.95
42501 Orange | 93.14 | 99.97
Success ratio is messages delivered to handsets, DLR ratio is messages that resulted in a delivery receipt - so for Pelephone, 99.99% of the time, your application will be sent a report notifying of the message status, even when it's not part of the 91.47% of the time the message is successful delivered to the handset.