MD5 (128-bit) and SHA-1 (160-bit) are obsolete for security because practical collisions exist. They remain in some legacy protocols but should be phased out in favor of SHA-256 or newer hash functions.
For passwords, do not use plain hashes. Prefer PBKDF2 or modern KDFs. For message integrity, use HMAC-SHA256. Maintain backward compatibility by publishing multiple digests during a transition.