Question: is it grammatically correct to say many a times?
Answer: "A" is a singular indefinite article, and "times" is plural. The two do not mix, therefore, it is wrong. "Many a times" may be a colloquialism, but it is still incorrect. "Many a time" and "many times" mean the same thing, but "many a time" is a more formal or old-fashioned way to say "many times".