That's a fungus gnat. I used to have a problem with those little buggers, which was the result of using substandard potting soil. Once I switched to quality soil and amendments, I rarely saw them again.

There's a pesticide called Gnatrol that's tailor made to kill the adults and the larvae, and it's deemed safe for vegetables. Neem oil isn't going to be effective, as you'll need to treat the soil as opposed to the foliar growth. The adults spend their short lives in the moist soil, and the larvae feed on the roots of the plant.

Another way to cheaply limit the spread of the population is simply to let the soil dry out almost completely, which will provide a harsh environment for the insects...and will lead to many adults and most of the larvae losing moisture in their bodies, and dying. If you have a bad larval infestation, you'll actually be able to see the dried bodies spread out all across the floor. The adults live for roughly one week, and are perfectly capable of laying 300-500 eggs in that time. And while the adults aren't very damaging to the plant itself, the larvae can be devastating to the roots if left unchecked.

The yellow sticky strips will also be effective in trapping a good number of adults.