I want to make an html form but I don't want to have an external program opened in order to send it.

Server-side scripting is the only way. Check out the ASP or PHP forums for email threads.

There are tons of free scripts out there that simply e-mail a form's data.

Check out http://www.hotscripts.com and look through there, specificly PHP and CGI as almost all hosts support both.

Hope this helps!
-Ross