How much sun are you getting? In my experience plenty of sun and water and basil flourishes.

Basil will grow in water on your kitchen counter if you have light. I have picked stems of basil, used the larger leaves, stuck the stem in a glass of water, and roots appear. Then leaves get larger and more leaves come. I guess that's hydroponics? Once there are enough roots, I transplant to a pot on the kitchen counter and gift it to a neighbor.

I have two plants in ground and insects do love them, but I share.

Full sun, plenty of water and plenty of room should do it.

It looks like too many plants for that size bed,

Plenty of sun and plenty of room (where the basil is). I started them from seed and thinned them out to 3 inches apart. The parsleys are a bit crowded but they don't seem to complain. That's why this is a big mystery to me.

It's possible you have basil downy mildew, a fairly new disease that is devastating to this herb. Check out this link, and Google for treatment options (not many).

http://vegetablemdonline.ppath.cornell.edu/NewsArticles/BasilDowny.html

Yeah, that's nasty stuff. I lost all my basil plants to it. Started more from seed and just set them out on the deck in cups last week hoping they will get big enough to be usable by the time the tomatoes are in full production. (I haven't broken the news to DH yet that that means I have to buy more pots LOL!)
Edie

Pick the tops off and use those leaves before they go to seed. Give them a little food and good watering and they should have some new branching in no time.

What are your night temperatures like? Where I live, the days can be quite warm but it is cool at night and the basil does not thrive. Some ways I have counteracted this is by growing near a stucco wall for the reflective heat or placing a milk cloche over the top until it fills out all the way. Since my nights are rarely over 60, microclimates are the only way for basil for me.

My Basil is awful this year and it's pretty disappointing because all my adult kids love it and are asking for it all the time. I put in a LOT of plants this year and they are all getting eaten. I would bet it is earwigs. I've had that problem in the past. I would go out in the night with a flashlight and there they would be eating away. Simple enough to just flick them into a cup of soapy water.

I'm considering growing them in my perennial bed next year to see if a change of location might help.

My basil was possibly the most successful thing in my vegetable garden. It didn't care about the cold nights, excess rain, or pest pressure eating the leaves.

I planted some in the front of my house as I had some extra seedlings, in a poor soil quality bed, with weed pressure, and that basil is doing very lousy, with thin curled leaves bolting to seed. I would suggest the soil/crowding is the issue based on my experience.

thinned them out to 3 inches apart

Way too close ... try 8-12 inches between any basil and the closest plant. Just clip out and use the plants that are between the final winners.

The parsleys are a bit crowded but they don't seem to complain. That's why this is a big mystery to me.

NO mystery. Parsley is not basil!

Everyone says basil loves heat. I disagree! 0nce the heat ramps up, the basil starts flowering! This makes the leaves smaller and more difficult to pick! NTT

They need also fertilizer, rich in nitrogen, well drained soil, water. It will take a while for basil to take off. If your plants are healthy, be patient.. fertilize them. Unlike some herbs, basil likes rich soil.

I consider basil to be a pretty short-term crop and start seeds three times during the growing season. I'm just ready to set out the last ones now.

I think the small-leaf varieties hold better in the garden. In your situation, I'd look at the globe basils, which are a great fit in raised beds.

This year my top performer has been Opal purple basil. The spring plants are still looking good, no so for the green Genovese.

Actually, I think I'll start a few to go through fall. We're usually still going strong through November. NT