Answer: Here are some possibilities; you'll have to play "garden detective" and look for clues as to the real culprit:
Cutworms -- usually attack young seedlings right at the soil line. Protect seedlings by wrapping loosely with newspaper.
Wireworms -- 1" to 1 1/2" long, slender, hard-shelled elongated larvae of the click beetle; chew on germinating seeds and underground plant parts. Try trapping them by burying a chunk of potato, covering it with few inches of soil, then placing a board over it. This should attract the wireworms; you can then dig up the potato and destroy the worms.
Slugs -- usually do their damage above ground, but might be a culprit.
You might also keep an eye out for rodents and birds that might be pulling up the seedlings.
Q&A Library Searching Tips