I use a monitoring service that sends out an email if my site goes down. How can I set up a script or something to where when an email is sent to say monitor@mydomain.com, it executes a website. At my cell phone providers site, you can send a text message to the cell phone, so is it possible to execute this url when an email is sent?

Dave,

A lot of cell phone providers give you an email address that emails can be sent to and they show up as text messages on your phone. I know verizon, voicestream, sprint, and At&t all offer this service. Normally the the email address is in the format of 2125551212@cellprovider.net

Yes, you should ask for email-to-sms (or text messaging) email-address from your cell provider. :)