The most popular algorithms of PoW-mining are:
1. SHA256 — it is used in bitcoin, all its forks, and some other altcoins. The main feature is that mining comes true only in case of ASIC’OV — special devices which “are ground” only under computation of this function.
2. DaggerHashimoto is used for ETC and ETH. It is effective on video cards. Quite detailed article about this algorithm.
3. X11 is used for DASH mining. Represents a combination of 11 cryptographic algorithms (blake, bmw, groestl, jh, keccak, skein, luffa, cubehash, shavite, simd, echo), from here and the name: X11. Only having cracked all 11 algorithms, hackers could receive control over a network. Code.
4. scrypt — Litecoin, Dogecoin and some other.
5. CryptoNight — Monero.
6. Equihash — ZEC, and BTG. Details.