DiscusFish/F2Pool

Officially known as F2Pool, this Chinese pool is also known as DiscusFish due to its logo — a discus fish. It is operated by Wang Chun and Mao Shihang, "two Chinese technology enthusiasts," Chun told CoinDesk in September 2014. A spokesperson told Business Insider that the pool owns no hardware itself; 100% of its hash power comes from users.
In July 2015, F2Pool generated the then-largest bitcoin transaction ever in order to clear up a spam attack of "dust" or tiny bitcoin transactions apparently intended to clog up the network.

AntPool

AntPool is run by Bitmain, a Chinese mining hardware company headquartered in Beijing. It boasts that its technology accounts for 56% of global bitcoin miners. It also claims to be the largest cloud miner in the world.
Bitmain was launched in Q1 2013, and co-founder Jihan Wu is the CEO.

BW Pool

BW Pool is another Chinese pool. It is owned by digital currency company Bitbank, which was founded by Chandler Guo, according to CoinDesk.

BTCC

A relative newcomer to the scene, BTCC (also known as BTC China) is one of the biggest players around despite only launching at the end of 2014. This growth is down to the fact that BTCC itself is one of China's largest bitcoin exchanges, and also offers a number of other digital currency solutions.
It was founded in 2011, and is currently led by Bobby Lee, who became CEO after purchasing the exchange in 2013.

BitFury

BitFury is the best-funded mining hardware company in the business, raising $20 million (£12.8 million) in July 2015. It was, CoinDesk notes, its third round in two years, and it has now raised $60 million (38.4 million) in total.
The startup is headed up by Valery Vavilov, originally from Latvia. It does not operate a public pool, but has private mines in Finland, Iceland, and the Republic of Georgia. Despite its prominence in the mining industry, Vavilov insists that "we are not a mining company, I don't like the word mining."
Instead, he told CoinDesk, "we're a technology company, but we're focused on bitcoin now. Our vision in the next three to five years is to move into different areas where computing power is valuable. We plan to expand into other fields of knowledge where humanity needs a lot of computing power."

BitClub Network

Unlike some other pools, BitClub Network does not disclose its founders, saying only that it is "run by a team of programmers, digital mining experts and entrepreneurs who have come together with MLM experts from around the world."
MLM stands for Multi-Level Marketing — a referral system whereby a user gains bonuses for each new user they bring in, who then gains bonuses for each new user they bring in, and so on. MLMs can be controversial because they resemble pyramid schemes, but BitClub Network insists that it is legitimate and not a "Ponzi Scheme."
For some users, it works as a cloud mining pool: Users don't have to own their own hardware, just pay to rent some owned by BitClub. Miners with their own rigs can also join the network, however.

Slush

Launched in November 2010, Slush Pool is the world's oldest public mining pool, and remains prominent today. Its formal name is Bitcoin Pooled Mining.
In real life, Slush is Marek Palatinus, a programmer from the Czech Republic. The pool is owned by SatoshiLabs, which also runs a number of other digital currency projects.

HaoBTC

HaoBTC is a Beijing-based bitcoin company that offers a wallet for storing the digital currency as well as a traditional mining service with a mine in Kangding, China. It uses its mining operation in a novel way: Paying “interest” to people who hold wallets with them with the bitcoins that it mines.
According to its website, it has “tens of thousands” of users.

KnCMiner

KnCMiner is a Swedish mining hardware company. It hasn't been worth mining bitcoin using standard consumer computer hardware for years because of the kind of processing power involved; the overwhelming majority of ordinary members of public pools will have bought hardware from companies like KnCMiner.
It raised a $15 million (£9.6 million) Series B in February 2015 led by Accel Partners. It boasts its green credentials on its website, and has data centres Sweden, with expansions planned for Iceland and Finland.

Kano CKPool

CKPool is a public pool created by an Australian anaesthetist and programmer, Con Kolivas, and bitcoiner "Kano."
It was launched in September 2014, and for risk-takers, it also offers a "solo" pool. This means that users will pool their resources to find a bitcoin block faster than they would alone — but only the user who discovers the block gets any reward.
This is the standard pool.