What exactly do you hash and how you use the hash?
Are you refering by any chance to storing account passwords for authentication with the site? The weackness of password hashing are caused by using the hash (any hash) in a wrong manner, not by inherent hashing algorithm weakness. Nobody is going to brute force your MD5 hash, the problem will be dictionary attacks agains known hash values (rainbow tables). And the protection is to use an HMAC hash, or something similar, like a salted hash.
I m afraid you re on the wrong track if you consider that using a different hashing algorithm will give you any benefit. While is true that SHA1 or SHA256 have stronger cryptographic attribute and will stand a brute force attack for longer time, even the stronges hash will be useless if incorrectly used. On the other hand MD5 will work just fine when used properly.