Like any other language, Objective Caml can be used to write CGI programs. The advantages of using OCaml for CGI scripting are the same a using OCaml for programming. The disadvantages are the fact that few CGI libraries exist for the language. One that sticks out in my mind comes as part of the OCamlNet library.
More to come...
It is almost trivial to set up OCaml scripting with Apache. The interactive top-level can be set up as a helper program and can therefore be used as an impromptu script interpreter.
Exact details on this to come...
It would not be hard to write a preprocessor in Camlp4 and build an true scripting engine (via a custom top level) in order to have OCaml function like a true scripting language, similar, albeit much more powerful than, to PHP. Code could be surrounded by special tags (maybe "<?caml" and "?>") and anything not within those tags would be echoed unchanged. Any takers? :)
Answer: It exists already, and it's called Camlmix :-) The latest version (1.3) allows one to compile such programs either as-is (the text is printed when the module is evaluated) or embedded into a render function that can be called by other modules.
For more permanent "deep-web" content, or for actions that need to be executed with significant speed (i.e., performing complex calculations), scripting may not be the solution. Compilation of scripts into binary format (especially native code) can give a significant boost in speed. Ocamlscript allows one to write one-file scripts that would be transparently compiled, when needed, using the native code compiler. So you actually can have your cake and eat it too. Ocamlscript version 2 fully supports packages installed with ocamlfind (Findlib), so that lots of fancy libraries could be loaded very easily, from the script.
The PPS Computer Science Laboratory has created Ocsigen, a web server and framework written in and for OCaml. The scheme is functions registered to a url, with pattern matching allowed on GET arguments, among other neat features.