Over on the ETJ list, Nick M. says that his student was marked wrong for answering "Yes, I have many teachers," to the question, "Do you have many teachers?" Nick wonders if there's some grammar rule that he's missing.
No, grammatically, "I have many teachers" is fine.
Stylistically, however, it is rather stilted, with 'a lot of' being preferred.
Pragmatically, it is both redundant in it's repetition of "(I) have many teachers" and uncooperative in it's failure to provide a shred more information than the surface form of the question requires. A more pragmatically appropriate answer would be something like, "Eight, if you can believe it."
Arnold Zwicky undertakes a quick survey of 'much' vs. 'a lot' over on Language Log. I think the issues around 'many' are quite similar; indeed, Zwicky touches on them in his explorations.