Is there a web application that will let me send SMS email? Some services don't seem to support receiving normal email.
Only the cellular phone carrier can decide whether you can send SMS via email or not. Here's how to reach people on the most popular carriers:
If you have some programming skills, you could make use of an SMS API (such as ZeepMobile or Twilio) and build a database associating emails to an SMS phone number. Then you could send emails to "firstname.lastname@example.org". The app would receive the email and redirect the message to the appropriate phone number.
I wouldn't recommend using the email to SMS function most carriers provide for 3 reasons: (1) the email address seem to change over time (I've had mine change with my carrier a few times) and (2) some carriers charge to receive email to SMS messages and (3) it's annoying to read, since I know some of them require you to respond with "Read" or similar before seeing the who message.
I've been using Twilio for voice and I've been quite impressed. I'm sure their SMS system isn't much different. You also wouldn't need to have much programming knowledge, although it would be a good idea to provide security.
There is also a similar quesiton on Pro Webmasters.