SHA-2 Family: SHA-512, which you mentioned, belongs to this family. Other members include SHA-256, SHA-384, and more. They are widely used and are currently considered secure.
SHA-3: This is the successor to SHA-2 and was standardized by NIST (U.S. National Institute of Standards and Technology) in 2015. SHA-3 is not a modification of SHA-2 but is derived from a cryptographic primitive called Keccak.
BLAKE2: An alternative to MD5 and SHA-2/3, it's considered high-speed and secure. There's also a successor, BLAKE3, which is even faster and maintains a high-security level.
Whirlpool: This is a cryptographic hash function that produces a 512-bit hash. It has undergone a few revisions and is currently considered secure.
RIPEMD-160: While it produces a shorter hash (160 bits), it's still considered reasonably secure and is used in certain applications like Bitcoin.
Argon2: Though not a general-purpose hash function like the others, Argon2 is notable as a memory-hard password hashing function. It's designed to be resistant against GPU-based attacks and is the winner of the Password Hashing Competition in 2015.