Doing so is quite easy. First you have to use Gmail. As it is a free service, you can create a dedicated account for your monitoring alerts. Once finished, login to your account and click on the “Settings” link located on the top right side of the browser window.
Then, select “Forwarding and POP/IMAP”:

As shown in the previous screenshot, the only thing you have to do is to check “Forward a copy of incomming mail” and fill the field with your phone number @ your provider service.
For example, If your phone provider is AT&T, you’ll have to type 0000000000@mobile.att.net.

That would be great, a free forward via SMS, but sad enough most european providers doesn't provide this "free" service. You can't send this kind of SMS, but maybe you can use some cheap SMS provider instead of paying high prices for SMS bundles to monitoring services...