Friend, the U.S. essentially invented low-fare carriers.
Southwest is the primary low-fare airline in the U.S., and in size, it ranks in the top 10 airlines in the nation. They're a an absolutely fabulous carrier, with low fares, open seating, friendly and courteous staff, and they make sure your flight is fun, often resorting to dozens of corny jokes over the P/A. I've flown them several times, and I'd fly them again in a heartbeat.
SWA is based in Dallas, Texas, but they fly from coast-to-coast, serving a mix of primary and secondary airports with their all-737 (200,300,500,700) fleet.
Incidentally, they could get you from LA to Washington, if you don't mind arriving at BWI, which is located between Baltimore and Washington. SWA is showing a fare of $402 R/T right now, seven day adv. purchase; you'll have to make 2-3 stops along the way. If you think you're getting from LA to DC for $200, you'd better start phoning Greyhound.
You can find out more information about Southwest at http://www.iflyswa.com
A short note about American low-fare carriers--generally, there are two seperate kinds: the deep-discount carriers (which fly for dirt cheap fares and fly into secondary airports, often with reduced service, open seating, no boarding passes, etc.) and mid-discount carriers (which fly for somewhat discounted fares, flying into primary airports, and offering service that's on par with the majors).
Other low-fare carriers are as follows:
: A deep-discount carrier, designed to lower airfares for business travelers in the Des Moines market, which is controlled by just a few airlines and has precious few alternative airports. Once bankrupted by running a moronic route structure that included stops in backwater burgs like Peoria. Recently brought back to life on government subsidies, with a partnership with ATA. Currently flies DSM-MDW, but plans to expand to New York, Los Angeles, Denver, and other large market airports. http://www.accessair.com
: A mid-discount carrier based in ATL, flying in the east using 717s, DC-9s, and one 737. Was formerly ValuJet, which merged with AirTran, a 737 charter operator out of MCO shortly after the Everglades crash in 1997. Offers business class, as well as economy. http://www.airtran.com
: A deep-discount carrier that flies DC-9s from Fresno and Long Beach on the west coast. http://www.allegiant-air.com
ATA (American Trans Air)
: Once exclusively a charter operator, ATA flies a combination of charter and scheduled deep-discount flights cross-country, utilizing 727-200, L-1011, and 757-200 aircraft. Hubs at Chicago Midway Airport (MDW) and Indianapolis, IN. Will replace the 727s and L-1011s with new 757-300 and 737-800 aircraft (with winglets on the 737s). http://www.ata.com
: A subsidiary of Delta Air Lines, Delta Express flies 737-200s in the East to Florida. A mid-discount carrier with deep-discount fares. http://www.delta.com
: Based at DEN, Frontier flies 737s (200s, 300s) from coast to coast. A mid-discount carrier. Well known for its lively and colorful aircraft tails, which feature scenes from the west painted on them. http://www.flyfrontier.com
: Based at New York Kennedy (JFK), jetBlue flies service to Florida, Buffalo and Rochester and a trio of cities out west (Ontario, Oakland and Salt Lake City) using brand-new A320s. A mid-discount carrier. Features in-flight PTV's in every seat. Currently the hottest up-and-coming airline in the industry. http://www.jetblue.com
: A subsidiary of USAirways, MetroJet also flies in the East to Florida using 737-200s. Deep-discount carrier. Has some routes that don't go to Florida. http://www.usairways.com/metrojet/index.htm
: The reincarnation of Midway flies out of Raliegh-Durham on routes in the east, using CRJs, F-100s, and 737-700s. Partner with American Airlines. Mid-discount carrier, well-known for its bright yellow tails. http://www.midwayair.com
: The reincarnated version of National flies out of LAS across the country, using 757-200s. Mid-discount carrier, known for their good service and friendly employees. Second only to jetBlue as the hottest up-and-coming airline in the country. http://www.nationalairlines.com
Pan Am Airways
: A mid-discount carrier that took on the proud name of the former PAA in 1998, Pan Am is based in Portsmouth, NH, and flies almost exclusively to secondary airports near large markets such as Boston, Chicago, Orlando, St. Louis, etc. Flies refurbished 727-200s in all-Clipper Class formation, which features increased pitch and legroom and inflight snacks. Three aircraft feature the graceful winglet hushkit system. Also flies charter flights. http://www.flypanam.com
Shuttle America Airlines
: A deep-discount carrier flying Dash-8-300s out of Trenton and Buffalo to a few selected destinations in the East. Recently started service from Boston Hanscom Field to New York LaGuardia. http://www.shuttleamerica.com
: A deep-discount public-charter carrier based in ATL, flying DC-9s to Charlotte, Tampa/St. Petersburg, and Sarasota. Also flies charter flights. Took over the National Sun King logo, after it changed hands a couple of times. http://www.jetsoutheast.com
: A deep-discount carrier based in Mirimar, FL, Spirit flies DC-9s and MD-80s almost exclusively in the eastern U.S., although they do fly one route from DTW to LAX. http://www.spiritair.com
Sun Country Airlines
: A deep-discount carrier based at MSP, flying 727-200s and DC-10s on a combination of charter and scheduled flights across the country and internationally. http://www.suncountry.com
: A mid-discount carrier subsidiary of United Airlines flying on routes in the west, primarily along the San Francisco-Los-Angeles corridor. Flies 737s (300s, 500s). Once called Shuttle by United. http://www.united.com
: A deep-discount carrier based at MCI, flying 737-200s mostly in the east. http://www.flyvanguard.com
If you want a cheap airfare from LA to Washington, it looks like your best bet right now is on ATA, which offers a fare of $248 R/T plus tax if you buy before Monday. You'd fly from LAX to MDW on a 757, and then change planes to a 757 or 727 to DCA.
Hope this helps!