Hash types supported by hashcat are categorized. These categories are shown in hashcat's extended help output (-hh). They are somewhat self-explanatory, but contain terms of art that may be unfamiliar.
A database file used “behind the scenes” by a general application (SecureCRT, etc.)
File archives (7-Zip, PKZIP, etc.)
Crypto wallets (Bitcoin, Ethereum, etc.)
MS SQL, MySQL, Oracle, etc.
MS Word, Excel, PDF, etc.
Solarwinds, PeopleSoft, Lotus Notes, etc.
Also includes web servers (Apache, etc.)
Such as ENCsecurity Datavault.
Drupal, Joomla, MediaWiki, PrestaShop, etc.
Django, passlib, Ruby on Rails, etc.
TrueCrypt, VeraCrypt, BitLocker, etc.
Some of these can have multiple underlying algorithms that can be configured by the user in a specific order, so quite a few sub-variants are supported.
Other general Key Derivation Functions (KDFs) - phpass, scrypt, PBKDF2-HMAC, etc.
Telegram, Teamspeak 3, etc.
NetNTLM, IPMI RAKP, Kerberos, SNMPv3, etc.
TOTP (Time-based One-Time Passwords), etc.
General and specialized OSes and their common user hash types, including network equipment, UNIX shadow hash types, etc.
LastPass, 1Password, etc. This includes password-specific DBs on the “back end” of applications and OSes (Apple keychain, Mozilla/Firefox, etc)
Special testing modes for which the hashes are not hashes at all, but the actual plaintext password. Used for debugging and research.
PKCS, SSH, GPG, Java keystore, etc.
File checksum algorithms traditionally used to validate that content has not been altered or lost, or is not duplicated. (CRC32, MurmurHash, etc.)
DES, 3DES, etc. See https://en.wikipedia.org/wiki/Known-plaintext_attack
Multipurpose general unsalted cryptographic hashes - MD5, SHA1, Blake, etc.
Raw (unsalted) hashes used for authentication / HMAC purposes (protecting a secret key). See https://en.wikipedia.org/wiki/HMAC
General hash types that are salted, or iterated/nested (SHA1 of the MD5 of a password, etc.)