Our big tomato is finally turning red and we found bunches of almost microscopic white bugs crawling all over it. Closer inspection shows more of them on other plants like basil and a few tiny, tiny webs. What are these critters and how do I make them die a horrible, screaming death? Maere sprayed a little vinegar and water on 'em. I personally don't think they need a douche. 
Yuck... More things probably die of a couple drops of detergent in a few ounces of water, than of vinegar and water. You might want to spray them with some detergent water tonight, just to prevent a population explosion before you get the real pesticides. 
Congrats on your tomato finally turning red!!!
We woke up to almost everything dead or dying, even my beautiful peppers are getting dead leaves seemingly by the minute. Now Maere can't remember if the spray bottle of vinegar was diluted or not or how much, if it was. <sigh> I gave them all a heavy spraying of water with a little dish soap but I don't know if it's going to do any good.
Bummer, Bruce!
Good luck salvaging them!
Possibly pure vinegar, eh? ... Might want to check the pH in the reservoirs?
PH and nutes are OK. I was going to EOL the tomatoes any day so that's no big loss and the herbs have been going almost 4 months so that's not too bad, it's my peppers that I'm hoping will survive. That plus wondering if everything else will get infected too. Here are some pictures of the carnage and a super closeup of the little critters, they are so tiny we'd never noticed them until Maere's daughter saw one moving... Spider Mites?



It does sound like spider mites. 

HELP!!! I found this little guy on one of my tomato plants this morning! What is it?
I dont think it was a lady bug. Its back was not round & I looked really hard before I killed it!

It looks like they're only on the tomatoes and basil, can't see any on the rest. Guess I'll make a trip to the hydro store and get something for 'em tomorrow then take the bottoms outside and give them all a good spraying. Ugh!