RSSI've just written this awesome script. Does anyone have [insert name of famous filmmaker]'s email address?
Internet Filmmakers' FAQ
Time for a quick reality check. If you were Spielberg (or any other famous filmmaker), would you leave your email address (or any other personal contact details for that matter) open to the public domain. Of course not. Think about it. For every one bona fide contact you got, there would probably be a thousand more from wanna-bes, fans, crazy people and even critics. You just wouldn't be able to deal with it. Unfortunately the more famous you are, the larger the "barriers" you need to set up between yourself and the general public.
Besides, even if it was possible to just email a famous filmmaker with your proposal, there are several other things working against you. Firstly and most importantly, for legal reasons they would not be able to even read your script - plagiarism is very real in Hollywood and people will do their best to avoid any possible exposure to such accusations. Secondly, regardless of whether your script is magic or crap, it may just not be the kind of project they are looking at doing at this moment in time. Finally, top filmmakers have extremely busy schedules and they may well be booked up until the end of time as we know it with other projects.
The best way to get your script to the parties you are interested in is through the proper channels (i.e. a damn good agent) or by using extremely creative means to have it "land" in the appropriate lap. The latter is of course considerably harder than it sounds as scripts are often read by many people before they are exposed to top directors. It's also worth considering what the individual director's approach to taking on projects is. For example, Steven Spielberg generally doesn't write his own screenplays, so it is probably 0.000000000000001% more likely that he would do your script than say, James Cameron, who pretty much always works on scripts that he has written. Basically, the best advice is, try by all means, just don't get too disillusioned when it doesn't happen. Make the film yourself!