Let's say there is a director whose movies you love, and the script you've written is just up his alley. What can you do to get that script in the director's hands?
First, if you have a membership to IMDB.com you can search the director's name and find out who his agent or manager is, then use the Hollywood Creative Directory to get the phone number to the office. Now once you make this call, you'd better be 110% sure of yourself, and have your pitch down so tight you can say it backwards and have it make sense. Because you will have to be quick and convincing to get a word in before the assistant or receptionist says, "I'm sorry, we don't accept unsolicited manuscripts."
And even though I shouldn't have to say it, be as nice and charming as possible to whomever answers that phone, because he/she may the next executive at CAA. If you can at least get your log line in before she gives you the "I'm sorry..." line, you may be past the unsolicited part all together.
If you have as good a pitch as a fellow screenwriter friends does, you just may get the assistant's email address, and now your script isn't unsolicited!
Yes, it's possible, but you had better be able to daylight to vampires if you want to try this tact. This technique isn't for the weak or unsure. So if you think you are up to it, "cowboy up" and do your research.
First impressions are lasting, so make a fantastic impression and whatever response you receive, be pleasant and thank the assistant for their time. Hollywood is a VERY small town when you are trying to break in, and day after tomorrow that assistant may the the director of the next box office hit. Don't laugh, stranger things have happened!
One caveat, some people will tell you this isn't a good technique and warn you against it. But if you have an incredible script and are comfortable selling yourself, it can be worth a try. Phone calls aren't recommended, but they aren't forbidden like in the literary industry.