I would never grow them like that! Just water them when they feel partially moist. Lift the pot when it is wet and lift it every few days. Wait until it is fairly light and water it until water comes out the drainage holes. It is a very easy plant to grow outside in the sun. You can save seeds from it when it flowers, which it loves to do! I keep most of my flowers cut off and leave a few branches flowering for the butterflies and bees.

Lunachic, First, where are you? That will affect how something grows. Upon first glance, to me it looks like the plants got too cold, but it's very hard to tell from a picture. Basil likes it hot! (below 50 is too cold--above 70 is really where they'll thrive). If you are in a cold weather place, the window may be too cold for the basil. It does also need a lot of light.

Second, I think you got two different 'types' of plants, for lack of a better term. The potted seedling from Walmart is meant to be planted up--that pot is definitely not big enough for the basil to thrive, especially since there are three plants there that I see. I would recommend a 12" pot for what I see. The others I'm guessing were the type that you can find in many supermarkets now that are grown more hydroponically, and not meant for planting or long life. They're meant to harvest all leaves for use right away. That's why no pot, and instructions for placing in water. They are not really meant to live once they're sold.

As for placing in the saucer of water, it's a common misconception--you'd think that since plants need water, then that would be ideal, and it probably is for a few types of plants. But, herbs do need the soil to drain to avoid root rot, and be watered as needed according to the plant's needs--basil likes to be kept moist, but not soaking if you see the difference. Your originaly potted plant may be saveable, but it is stressed right now--needs a bigger pot and more light from the looks of it.

The non-potted ones drowned; toss 'em. They are not even edible at this point.

There IS hope for the potted one, but get it OUT of standing water as Zackey suggests. Never allow any potted plants to stand in water. (But do not let it dry out entirely, either! The light mix the nursery uses, once dry, is almost impossible to re-hydrate.)

The basil in the pot is actually 5-6 plants -- way too many for that size pot. In the garden or good-sized container, one basil plant can get a couple of feet tall and at least a foot wide. It would be chancy to try to separate them at this stage of their growth but you could try cutting each one back just above the lower sets of leaves and try rooting the cuttings in water. But you must not allow any of the leaves to sit in water or they will rot as the Harris Teeter plants did. If they do send out roots (sometimes they do, sometimes they don't), once the roots are about an inch long you could carefully pot them separately using a seed-starting mix (NOT backyard dirt or even potting soil--those are too heavy). Seeding mix is peat, vermiculite and perlite. Don't use fertilizer at this point. If you can get some good compost or worm castings, mix some of that in.

The potted plants are "leggy" -- too tall because they are not getting enough sunlight. Even a south window (especially if screened) does not provide the sun a basil prefers for good growth. With luck, your plants will survive long enough to plant into a larger container and go outside when the weather is totally warm (consistently above 50 degrees at night).

And if you want success at growing plants, start reading & learn how to do it! Tons of good info on the Web.
Good luck.

I've had several of the herb plants root that are meant for leaves only. Most have a good root system even tho it is quite small. But I always put them in a 4" pot to start.

Yes they have drownor gotten root rot. Give the living one a larger pot & fresh soil and don't let it sit in standing water. Give it a while to recover & show new growth before harvesting from it.

At first glance it looks like the smaller plants have root rot, but what jumped out me first was they all should have been potted in larger pots. I don't think it's possible to save the smaller plants so I would just put them in the trash, but I would save the larger one.

The large plant looks a bit leggy to me, so I would first get a larger pot and fill it with potting soil. Then I would cut the stem into 3-4" cuttings, making sure to leave at least 2 leaves near the top so the plants can re-establish themselves. Then I would stick the cuttings in larger pot(s), And if it looks like one of the stems is about to flower (small white flowers at the top of the stem) I would pinch them back. Otherwise you will wind up with a woody plant.

Also I would never place basil in standing water. Basil is especially prone to root rot as seedling, so that is something to keep in mind.

Hope this helps!