How do I evenly emit particles from a surface? Check out the image below:



Notice how the particles are emitted in distinct streams. What I need is for the particles to be emitted in the shape of the mesh they're coming from. I've tried all the options I can think of to get an even distribution but nothing seems to work. In particular, I was hoping that increasing the amount of subdivisions on the emitter would help, but no dice.
Increasing the subdivisions of the mesh should help, you will just need to make sure the subsurf modifier is above the particle system and then check 'Use Modifier Stack' in the particles panel. 

Another option is to add some random velocity to the particles in the Velocity panel. It seems (based on brief testing) that adding random velocity will produce nicer results when emitting from volume as opposed to faces.