Scam. If you don't think you have an Adobe account, you probably don't. The free Adobe products (Reader, Flash, etc.) don't require an account.
Activating their non-free products (Photoshop, Premier, Illustrator, etc.) require an Adobe account. The scammers probably want access to your license keys, etc., in addition to possibly buying crap from Adobe with your credit card (can't remember if the account retains CC info when you buy product digitally).