We have configured email alerts in our environment. Recently I had requirement of sending SMS for critical alerts on production server. Though this is NOT a feature of SQL Server, but we have a simple workaround for this.
Cell phone service providers have a SMS gateway. These gateways accept requests via email.
To send sms to any mobile number we need to send email to this gateway. I have IDEA connection and was successfully able to receive sms on my cell by sending mail to below gateway :
You can quickly check by sending mail to this from your gmail account.
There is a list of gateways I found on below link :