Okay... I don't know those bugs.... so I can't give you a specific killer for them. BUT you said that insecticidal soap didn't work.... hmmmm... what is the main ingredient in this soap? Pyrethrin? Pyrethrins should work, they kill most little buggies. And it is biodegradable, so that you can eat the basil afterwards, but I'd wash it anyway.
They look like they fly, can you put some netting over the basil? or maybe use some fly tape" see if they stick.

Yes you are right, they have wings but I didn't see them fly. Their movement is pretty slow even when I try to touch them.

I am not sure the insecticial soap's ingredient. I noticed after I spray on the plant, a lot of leaves changes color and the next few days, about 50% of the leaves droped to the ground. However the bugs are still there.

Have tried using water hose to get rid of them but no effect. They cling very tightly to the leaf.

The sticky tape might not help because these bugs do not hop and there might be hundred or even thousands of them. The picture shows the adult. The young ones are smaller and difficult to see, about 0.2mm in size.

Any help would be appreciated.

Hi Have you tried spraying Rubbing alcohol? You can get them anywhere. The 70% rubbing alcohol is a contact poison for some insects.

I think I know what you've got there, I think it's what I've got on my basil too. But I couldn't get a good zoom in on the picture.
Do they have an alligator look? Like this:
http://www.celticbug.com/Real/Bugs3.html
They can also be more reddish in color. If so you're good; leave them be; and thank good you were blessed with these little bugs.
If they don't look alligatorish.
I'm sorry, you've got aphids. I'm dealing with them too. And they've been having a field day with my basil. If your basil is just ornamental seven-dust the hell out of the seedlings. If you plan on using the basil in food though you can try on a couple of other solutions.
Plant mint, rosemary, marigolds or sage near the basil supposedly aphids don't like the aroma of these herbs this worked some what for two years ago. But last year when the aphids came back again, I tried lady bugs. They worked really well but the problem with them is that they fly away after they've eaten the adult and larvae aphids and when they're gone the aphids eggs hatch and you've got aphids again. My gardening store recommended I try green lacewings which aren't as migratory as ladybugs so they'll stay with the basil. You have to mail order them so the lace wing should arrive in the next day or so; so I'll let you know how they work.

Also if your basil is in a pot move it as far away from any roses as possible, since aphids love roses too.

I have got better pictures so that you can have a better closeup on the bugs. It is not alligator like and definitely not ladybugs. Not aphids either because these are black bugs.

http://public.fotki.com/gaku70/bugs/

Hope someone can help fast before all my basils dies.

Try rubbing alcohol already but bugs came back the next day. Another basil died on me...sign!! Please help!!

I'm so sorry to hear that, I had those little guys all over my basils last year, it had gotten so bad that I just had to get rid of the whole plant :( I really hope that you'll have better luck than I did.

an insect, green body 1/4-1/2" long, red dot on top in center, red feelers or legs or whatever on each end of insect...creates a stinging sensation when in contact to skin. it swelled my vein in my hand double size and it kept traveling (the swelling) to my wrist and forearm, making my hand shake terribly. Went to our local Multi-care unit, he said it was an allergic reaction, gave me a shot of Prednisone, which eased the stinging sensation and reduced the vein swelling. What is this insect? never saw it before, been gardening over 50 yrs. It's a clinger, have one on a piece of paper towel, doesn't move much..unless you touch it with a pencil, it's feelers move, they must be what causes the stinging sensation?

Got a photo??

I found one of these on some basil - i got bit also. I put meat tenderizer on the bite - like you would for a bee sting - and it seemed to help. Anyone know what this bug is? Body looks to be about 1/2 inch long.

Here is a link that might be useful: Photo of the bug

Place 2 or 3 cloves of garlic in your soil.
Bugs do not like garlic.