Could be any chewing bug, or slugs or snails. They just love eating baby plants of any kind! Sprinkle some bran or sawdust around your babies to prevent the creepy chompers, and make a little tent with some mosquito fabric (the kind you cover your baby's cot or pram with) to keep away the flying chompers.

You could try cutting the top and bottom off a plastic soft-drink bottle, or a cardboard milk container and put it over your babies. Makes the plants harder to find and get at.

You could also try spraying your plants with some garlic spray. So you can't wait for a week? Use it straight away! It won't affect the flavour of the plants, but yours aren't ready for harvesting yet anyway. Keep up the spray about once a week or so if you've still got thieves - just wash the leaves as you would normally before using them if you don't want the garlic taste.

GARLIC SPRAY:
Soak 1/2 cup crushed garlic cloves in 1/2 cup vegetable oil for one week. Add a little liquid soap and dilute the mixture - 1 part mixture to 10 parts water. Garlic spay will kill and repel aphids, woolly aphids, bean fly, stink bugs, crickets, grasshoppers, red spider mite, sawfly larvae, scale, snails, slugs, thrips and caterpillars, mosquitoes and ticks, the adult moths of leaf-miners and mealy bugs. It is an effective fungicide when used 3-4 times a week against potato blight and damping off.

Could be slugs. I HATE slugs. You can make little copper collars for your plants. Think of a mini chimney about 3 inches high around the base of your plant. Slugs won't cross the copper because it gives them a little shock due to the slug's sliminess. You can also sprinkle diatomaceous earth around the soil. Don't get the DE used for pools, this has been treated and won't work. Get the DE used specifically for slug control. It is totally organic and won't hurt you or your pets. Good luck!

also, my favorite... a shallow bowl full of beer... the slugs flock to it and DIE DIE DIE! :oD

I'm having trouble with the birds eating the new sprouts.

Sadly, all of my baby plants are gone. I woke up the next morning after writing the message, and went to check my plants. The bugs had gotten away with my last 2 babies. Now, all of my hard work for the summer has completely gone to waste. I don't have any baby herbs at all. My Basil was the only thing that was making it.
Well, atleast next year I will know how to keep the critters out.
Thank you for all of your replies.
AR_Dramaqueen

It shouldn't be too late for you to plant basil again this year. With your growing season you should have at least four months or more of warm weather.

You might be able to find new herb plants at a Farmer's Market, or possibly a nursery. I think I'd put my herbs in large plastic pots that you can set into your garden. If it is bugs, that will stop them, but if it's a larger critter that's another story.

They were in pots. They were in pots that sit on the railing of our deck. The bug just got into the pot.
Maybe I can talk Mama into buying me some more seeds. It was bugs though. My dad saw the creepy crawly snip the top of one baby plant, but he could not stop the critter from going below the dirt. I doubt it was an ant because he said he didn't know what it was, and he knows what most outside stuff is.
Maybe I can replant. Mom will just have to wait longer for her herb garden.
AR_Dramaqueen