Chris

I have them on my tomato plants, too, but I haven't seen any damage so I don't try to kill them. They seem to like to hang out between the hairs on the stems. Their name is probably "fungus gnats", but unless you have sickly plants covered with them, the healthy plants aren't likely to be bothered by them. I believe they're attracted to the moisture on the tomato stems.

Fungus gnats are usually more of a nuisance than a problem. The biggest trouble is the larva can root prune baby seedlings.

Thanks for the input anney & timmy1.
They may have arrived because of the straw mulch I am trying this year. No problem.