Once a story/picture/music becomes fixed to media--paper, recording, film, etc.--it is technically considered copyright of the owner IF it is an original work. Ideas, per se, are not copyrightable. Names aren't copyrightable. However, trademarks exist to cover many things not covered by copyright.
While there are strong opinions in many ways, my own practice is to keep a string of copies as I edit the work. This shows both its origin and a continuity of work. Someone could say, "Well we had this idea in 1993." If my records show, that I created it in 1984 with revisions through out. That I shared that idea with the company in 1992 for consideration, it makes for a stronger case.
Because copyright is more enduring, I think of it as "concrete". That is, it is only protecting the manuscript as submitted--word for word, basically. So if the manuscript is being revised, you'd have to copyright each revision at a cost.
Most countries have Writers Guilds which provide registration. Registration is more flexible. Often you can make minor revisions. The registration can be used in a court to help establish some priority. It often is only good for five years and can be renewed. Many companies or services require you to have your script copyrighted or registered. There are independent services that also serve as "registration banks".
Before submitting a script, it's usually a good idea to have it registered. While what others say is true for movie companies, most of the complaints I've read on forums are individuals or start-ups looking for a script. Big companies have their choice of scripts and a stable of writers, so they are not going to play games.
I did read of a writer who responded to a Craigslist ad for a script. The 'producer' never wrote back. After pursuing it, the writer found that the guy collected scripts, doctored them, put his own name on them, and submitted them. Some of the script services don't screen who has access to your manuscripts. [I believe I read this on Absolute Write bulletin board but I can't find the citation. Sorry. There are a number of scams aimed a screenwriters eager to make the break. "If it sounds to good to be true, it probably is." Especially if they want $$$.]
Now as pointed out, this really only becomes an issue if the 'middleman' manages to successfully sell your script. Maybe s/he deserves the commission.
But for the production company, they may be suckered and not know s/he stole the script. Having the records will help you support the argument of creative origin.
Bottomline, once you've revised your script to the point you're confident to submit it, then you need to make the decision. Registering is a good first step. If it is optioned, the producer will likely want to copyright the final script along with the subsequent production. If you do copyright it, it grants you certain additional protections and rights--such as sequels and adaptations. However, you will likely need to transfer many of those rights.
The cost of registration is similar to that of copyright in the US about US$20. Registration with the WGA is very quick and you receive your registration number immediately.
While most companies think it's amateurish to put a "(c) 2011, I.M. Author", most don't think too much about a "WGA 19302345" under your contact info. Many entertainment lawyers encourage you to do both. Many industry insiders suggest you do neither on your cover page.
If I'm sending a manuscript to an established company or agent, I'd probably leave them both off. Often in those cases, they have you sign an agreement prior to reading your script. If I'm sending it to an unknown individual or smaller company, I might have the registration listed as a deterrent. There will be a spectrum of opinions.