Can insecure algorithms be combined to form a secure algorithm?
At the time of answering, the question was can insecure algorithms be combined to form a secure algorithm?



Yes: Think of any secure round-based block cipher. The independent rounds are not secure, but put together the overall cipher is. I think my favourite example is (currently) the Even Mansour cipher,
which combines two xor operations and one unkeyed permutation to form a secure cipher.

 nb: I know this isn't a direct link, but its the best introduction I know of

For a good discussion of the hash example in your question, read this question.