Which other methods to send mail from a form?

I just know mail function, like: mail(string to, string subject, string message)

Has anyother?

The mail function provided by default in PHP is more than enough to fit all the needs of a programmer concerning this. In order to get other mail functions, you would have to install some PHP mail modules into your server or when compiling PHP from source.

but many server do not accept mail function, and other alternatives is necessary

I believe Trap17 servers allow mail() function, I'm not sure, as I didn't have the need to use it...

And since you do need to install additional libraries for PHP, and recompile, you won't be able to do that, until you run your own server, because most hosts run only the default PHP binaries, with maybe few additional functionalities included...

mail() function is more than enough to send an email automaticaly, from your script... Move your hosting to Trap17, and you'll be able to use mail() function...

I've tried it and the mail() function works great. I think it's all anyone would need and like Galahad said, you wouldn't be able to install PHP addons unless you were running your own web server in which case you could just enable the mail function.