Pac-Man is a Japanese arcade game released in 1980 by Namco and published in North America by Midway. Namco released numerous sequels and spin-offs, many of which have also been remade on multiple platforms, including home consoles and handheld devices. The first sequels were primarily released in arcades, while later titles were released on video game consoles.
There is a series of JAKKS Pacific Plug & Play controllers that are Pac-Man themed. Most of them feature either Pac-Man or Ms. Pac-Man as the main game and then include other Namco arcade games with it. Bandai also released their own in 2012 called Pac-Man Connect and Play.
There are also many compilations featuring Pac-Man that don't have Pac-Man's name in the title. The most popular example is the Namco Museum series (every Namco Museum title features Pac-Man as the mascot, even on the few rare moments where the original Pac-Man game is not included) which has been on almost every video game console since the fifth generation, a list of many other Namco compilations (most of them featuring Pac-Man in some way) can be found here.