I was recently quoted Alex Epstein's blog about querying. In regards to some of the comments, I thought I'd expand a little:
Yes, there are instances in which people respond to query letters. This happens when 1) your query is short, well-written and makes your script sound very interesting, and you do not ramble on about your life as a pig farmer or whatever - and 2) you happen to send the letter to a person who is looking to find new clients and read unsolicited materials.
Remember that most query letters will go to assistants, not the agents themselves. If the assistant is an aspiring agent (perhaps even an agent trainee) and wants to find material to impress their boss, they'll probably respond to interesting query letters. However, most agent assistants I know do NOT want to be agents. They are doing their "year at the agency" so that they can move on to work at production companies, studios or networks, or because they're writers themselves who want to learn and make contacts to start their own writing careers. The aspiring producer/execs are probably busy reading every project that's sold, every project that comes in for their bosses' clients to rewrite or direct, every script the clients write, etc. and aren't really scouring the earth for new material. The aspiring writers are probably not going to pass anything to their bosses unless they think it's the greatest script they've EVER read EVER because the only thing they're ever going to give to their boss is their own script. This is how I feel, at least. Because if I pass my boss a script he thinks is crappy, he's not going to trust my taste anymore. Now, if someone sends me a script that absolutely blows me away and I know my boss will flip for it, I'll pass it on. Have I ever read such a script? No.
Also, even if you do find an aspiring agent or agent trainee, you still might not get that far. Think like an agent for a second. Remember that agents' first priority is servicing their current clients, not finding new ones. And when it comes to new ones, at big agencies at least, they're looking for people who already have credits, already have managers, etc. Building someone's career from absolutely nothing is hard work, and they're only going to take the risk if they're really confident about the person. Even junior agents who are often labeled as "hungry" are expected to be out finding work for current clients or pursuing hot clients represented elsewhere. Plucking new writers from obscurity is never going to be the #1 concern. (Now, I'm talking about people with absolutely no heat or name recognition. If you win the Nicholl Fellowship or a well-known producer options something of yours, pursuing you will instantly become more important.)
So if you want to query, go ahead. I'm just telling you...the way I see it happen 99% of the time is that people pass along scripts written by their friends and colleagues, not people they don't know.
I also have to disagree a little with Alex's suggestion of saying "__(insert executive)__ suggested I email you." Because if you really have a relationship with that person, then that person will call or email the agent first on your behalf - and you won't be an unsolicited query anymore.