It is possible to be your own literary agent. I don't personally know anyone who has gone that route, but I do know it's been done.
1. Search out publishing companies that accept unagented, unsolicited manuscripts. There are lots that say they do, but whether or not your manuscript receives more than a cursory glance is hard to determine.
- Heather Osborn an acquiring editor of Tor Books (imprint of Tom Doherty Associates, LLC) is looking for paranormal romance or urban fantasy. She suggested Stacy Hague-Hill (Thanks to twinkiethekid for spelling advice) as someone actively looking for Science Fiction / Fantasy aquisitions.
- Check out Fleetwood Robbins, an editor at Wizards of the Coast, as well.
- Ace & ROC of Penguin Group will also accept direct queries from authors.
2. Do the research. Each of these publishing companies details specific guidelines for submitting your work. They're all different. Look up what they want, do a google search for an editor to send it to, and then personalize the query letter.
3. Find out what it takes to represent your own work. I would recommend Martin P. Levin's book Be Your Own Literary Agent: The Ultimate Insider's Guide to Getting Published. While not the final word on the subject (chapter on contracts advises finding a lawyer or an agent) , it will still give you some tips on getting an editor to look at your work.
Are you someone who has gone the unagented route? What were your experiences? Did you find that getting published led you to an agent? Or did you decide to continue on alone?