What are the important points about cryptographic hash functions?

Question

I was reading this question on MD5 hash values and the accepted answer confuses me. One of the main properties, as I understand it, of a cryptopgraphic hash function is tha

Answer 1

These are the properties of hash functions in general.

A word of caution though, MD5 shouldn't be used anymore because of vulnerabilities that have been found in it. Check the 'Vulnerabilities' section and external links detailing these attacks. http://en.wikipedia.org/wiki/Md5 You can make an MD5 collision by changing only 128 bits in a message.

SHA-1 is safe for simple hashing although there are some attacks that would make it weaker against well-funded entities (Governments, large corporations)

SHA-256 is a safe starting point against technology for the next couple decades.