Do all cellular companies have open APIs that allow them to send SMS messages like Twitter?
Do you need to pay for it?
Many (most?) Mobile companies have email gateways that allow them to send SMS messages. For AT&T, I consider phonenumber@text.att.net , but each provider will have a different address.
This wikipedia article is good enough. Some cellular companies have simple formats. For example, Verizon uses number@vtext.com.
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Clickatell http://www.clickatell.com/developers.php
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