How would SSL help you? That would only secure what people want to send your script.
If you don't allow the "To:" to be set by the visitor that's making it a bit easier :) Just don't send a copy to the address the visitor states to use in the "From:", as this could be misused too.
A few other ideas:
You might want to use a "(un)check this option to prove you're not a script"-checkbox. This at least knocks out the poorly written scripts.
Check all fields strictly. Think about the possibilities for an attacker if he finds out he can add newlines to the header section of the generated mails ;)
If you use other people's scripts, check the code.
This is by all means definitely absolutely not complete.
Ordinary morality is for ordinary people. -- Aleister Crowley