What strategies are most effective for Symmetra turret placement?

I place turrets around door frames or on walls/obstacles that enemies are likely to run past. For example, the payload maps have flanking routes that connect to the main path via a doorway or narrow passage. Drop your turrets to surround it so that someone trying to flank will get zapped the moment they set foot through the door. A (not good) example would be the mining tunnel at the start of Route 66. Doorways are good because the majority of heroes will have to step into them in order to clear the turrets. Another decent spot would be the KotH maps that have ceilings on the control points, such as first stage of Illios or second stage Nepal. You want the LoS to your turrets to be as short as possible.

Watch the routes the enemy is taking and place turrets in the blind spots on those routes. As you play the maps more, you'll figure out the most popular routes and that will in turn help you figure out where to drop turrets. Symmetra isn't the best for getting up in the thick of the fight, but she is really good at protecting flanks.

Depending on how far away your team's spawn point is to the map objective, it can be more useful to use some of your turrets to defend your teleporter rather than the actual objective. In general, this means you'll want to find a place that's easy for your turrets to defend while being close to the objective to place your teleporter. Menace's answer covers some good points, but here are a few in addition to those:

Try to find archways or doorways where you can have turrets in different locations that can all hit the choke point. Good teams will fire explosives through the door before going through when they notice you are placing turrets, so you want to minimize how many turrets can be destroyed per explosive.

On attacker/defender maps (where one team defends two points), it can be just as useful to use your turrets to deny an alternate route to the point as it is to put them on the point itself, so that the enemy team has to use paths that are easier to defend. These maps also usually feature a very long runback for the defending team on the first point, so keeping up an active teleporter is just as crucial as any other turret use.

When you are standing on your defense point and the enemy team is right there, try to choose places where the turrets will at least distract them long enough for your team to fight back. Focus on putting down a lot of turrets in OK places rather than trying to get to a good place, and practice hitting slowed targets while moving around with your charged shots. Also, if the point has any walls, try to place a turret or two behind the wall - even if there is some piece of the point it doesn't cover, tank characters often will charge to the back of the point and focus on zoning your team, and will then get slowed and killed while the rest of their team can't hit your turret.

Nobody else has mentioned this, but planting turrets on static and dynamic props can really make it hard to find and easy to gain free meter.

For example, on Route 66, Stage 3, the rotating platforms that hover on the top can be used to place turrets on. One strategy I use all the time is the "Rotating Sushi Table", 1 turret on every platform. That way, as attackers attempt to push the payload they are struck with lasers that slow them down and cycle over and over.