I've been very happy with Twilio, but setup on their site is NOT for the faint of heart. Probably took me 10 days to get it done right... First, I have no idea what I was doing, and 2nd while their tech support was VERY helpful, and continued to work with me until everything was working, it did take a day or two, or longer for them to reply.
Twilio isn't free, but it is so damn cheap as to not really matter. There are lots of pieces to the puzzle spread over their website. Honestly, Twilio is really built for much bigger operations... sending out SMS messages is below kindergarten in their book, but it can be done.
It's been awhile since I set this up but if you need help or more info, PM me and I'll see what I can do.