Does anyone know of any SMS APIs that I can use in my web application to send SMS messages to users?
Most mobile providers support SNPP (Simple Network Paging Protocol). Despite the name, SNPP is also used to send text messages to cell phones. It's really easy to use. Just determine which mobile provider each user is using and then dispatch a "page" to the corresponding SNPP server.
For example, Sprint's SNPP server is snpp.messaging.sprint.com:444. The basic process goes like this:
Some servers also support subject lines and delayed messages, along with two-way messaging.