If the sun's a factor, and the winds are light, the tower almost always uses the runway that had the pilots looking into the sun so that the controllers don't have to.

Nothing much to add since everyone has chimed in so much.

However, every pilot will tell you it's based on weather - wind speed and direction. If winds are dead calm and don't favor one particular runway, it's usually a convenience of departure corridors, traffic, etc.

I don't know any way to guarantee you will have a particular runway in advance. Things change. If you have an active runway, say 24 (meaning 240 degrees magnetic), and the winds change to favor runway 18 (180 degrees magnetic) then that's what will happen. Or a controller may opt for a particular runway or change it due to traffic or other.

If you are on the ground in the terminal before you board, and have a radio that picks up aviation bands, you can tune in to that particular airports ATIS (Automatic Terminal Information Service) to try and see what the winds are, and if there is a runway or runways being used. Then you could try and change your seat based on this before you board. At very large airports, like ATL, this is going to be very hard to guess even with ATIS.

Good luck!

The strategy I'd use it to initially request the seat based on the prevailing wind direction. Then when arriving at the airport I'd watch which runway(s) the planes were using and change if required.

At LAS, when it gets above 100F, planes will favor departing Runway 7 because of the slope and the lift.

At SAN, heavy departures (transcon) prefer Runway 27 because of climb rate requirements. On foggy mornings, when they have to land on Runway 9 because Runway 27 doesn't have ILS, they'll still depart on 27. Once the heavy departures are done, they go purely Runway 9 until the fog improves.

It's easy to figure out at SNA, with only one runway used by large planes. Most of the time flights are southbound, though they will switch it if the Santa Ana winds pick up.

Just search (for example ctrl-F in Internet Explorer) for ATIS. But, since ATIS is usually updated each hour you may have to call the number each day for the few days preceding your flight day around your flight time to get an idea of what you'll probably get on your flight day.

Let's not encourage PAX to call the ATIS! It can sometimes be challenging enough to get through for real pilots that have a valid reason to call the ATIS/AWOS.
I'd suggest a trip to http://aviationweather.gov/adds/ click on TAF tab, type in the airport of interest, check TAF and METAR and select the translate option (if you don't understand the abbreviated version). This will give the current conditions and the forecast every 6 hours for the next 24 hours. Don't forget to put K in front of US airports (look up the ICAO designation for non-US airports).

Or you could just look out the window at the airport and see which runway the other planes are using.

Good point! Although I'm usually picking-up the ATIS via radio anyways. It's been a long time since I've called a phone number for the ATIS.

You might use FlightAware to see if there's a pattern you can see for your particular flight. If it's predominantly in one direction, you might gamble on that. It's better to check flights at your actual departure times, as some airports have prevailing winds that vary by time of day.

Prevailing winds give you the odds. Odds on, of an westbound landing/takeoff in YVR and LAX (don't think I've ever had a eastbound landing/takeoff at the latter), and a southbound takeoff/landing at SEA.

In California for airports near the coast (e.g., LAX, SFO, SJC, OAK, SNA, SAN), the wind almost always blows from the west or northwest. Therefore, takeoffs and landings are toward the west or northwest unless there is a storm (usually, only in the winter months).

when one flys tatl on biz class at least on ua, one can frequently lay with head fwd. very weird sinsuation to go "backwards".