The companies that mass produce the discs are "first-party" companies: Sony (for PlayStation consoles or handhelds), Microsoft (Xbox), and Nintendo (Wii). For PC titles, it's usually the publisher's responsibility for mass-producing the actual discs. Example publishers are listed in Geoff's answer above.
Whether or not these companies outsource the actual manufacturing or whether they have an in-house division, I'm not sure. When I worked at EA making console games, we would finish the game on our side and then submit it to the first-party (Sony, Microsoft, and/or Nintendo) for verification. Once it passes first-party certification, it goes on to manufacturing. We would usually receive a sample disc, usually called a "silver", to play through and test to make sure it works okay. Once we verify it works, we let the first-party know and they go make all the discs.