What are these bugs and how do I kill them?

I think they may be plump little aphids. It is easy to kill them if you go nuclear on them with insecticides. I am sure you can find organic/friendly concoctions on-line that can control or limit their populations.

I take buggy plants outside and blast them with a hose to physically remove bugs. You can also use a http://www.ehow.com/how_7265862_make-insecticidal-soap-spray-plants.html. Both need to come in contact with the bugs to be effective. You'll have to repeat this every week or so. Avoid fetilizing with any nitrogen, as it attracts pests and pathogens. The fungus gnats are harder. The dryer you keep the soil, the better. You can use a http://www.ipm.ucdavis.edu/PMG/PESTNOTES/pn7448.html with Bt specifically for fly larvae. Bt for caterpillars will not work.

Oh, and the bugs look like aphids of some type. Maybe wooly aphids, but it's hard to tell from the photos.

I think they may be http://en.wikipedia.org/wiki/Mealybug. Nasty little buggers. Unfortunately, I have no idea how to get rid of them and have had to throw away 2 basil plants because of them :(

I rid my rubber plant of mealy bugs (looks like them!) by washing it with hot soapy water (just normal dishsoap) thoroughly 2 or 3 times. I don't fancy doing that to basil.

Look like aphids that were on my pepper plant. Neem oil/soap spray is what I used to good effect.

Thanks, I made the homemade spray and am going to try it now. If it fails, I will order Neem or Safer's.

I've done the Bt soil drench thing to great success with some buggy houseplants. Buy a pack of http://www.lowes.com/pd_92460-1643-MODU1_0_?&productId=3047384 and drop one into your watering can. Fill it up and use it to water the plant and thoroughly wet it down with the stuff.

You have to persevere with the fruit fly trap until they're all gone, because each female can lay hundreds of eggs. Give it at least two weeks. If you still have flies, give it another week. You also have to eliminate the places they can lay eggs, like fruit or other food or dirty dishes on the counter or in the sink, and flush out and/or cover all your drains, because they will lay eggs in there too. They will lay eggs anyplace that is moist and has the tiniest bit of organic matter - dirty sponges and washcloths, juices, spills and messes, open trash cans, the dishwasher, that leaky spot under the sink - you get the idea. I found that while the paper-cone-in-a-mason-jar-with-cider-vinegar trap was effective, it wasn't nearly as effective as when I added a drop of dish soap to the vinegar. This breaks the surface tension so the little pests don't just get trapped, they drown. With the dish soap added you don't even really need to use a paper cone - you can just set out several uncovered bowls or jars of cider vinegar with a drop of dish soap, or cover the bowls with plastic wrap with some slits poked in it. Place them near your plants. Leave them alone until the flies are gone.