Mappy - Platform-esque - (mappy, mappyj) - Play as Mappy, a mouse who is a member of the Micro-Police, as he braves a house occupied by the cat-burglar Nyamco and his hench-kitties, the Mewkies, in an attempt to retrieve stolen goods. If you can manage to pick up the matching pairs of items in sequence without getting yourself killed, you can score big points.
Pac-Man - Maze - (puckman, pacman) - As far as I'm aware, this was the first video game to star a hero character (rather than a vehicle of some sort). You must guide Pac-Man around the maze, eating dots and the occasional piece of food that appears, and avoiding the four ghosts, Inky, Pinky, Blinky, and Clyde. You can turn the tables on the ghosts by eating a Power Pellet - then you can eat them, too! (The Engrishy-named bootleg,
Hangly Man, apparently provides an interesting variation on this game's mazes.)
Ms. Pac-Man - Maze - (mspacman) - This game is much like Pac-Man, except you play as Ms. Pac-Man, and the gameplay is more refined. The behaviour of the ghosts (Inky, Pinky, Blinky, and Sue) is more random than in the original game, and it takes good reflexes to outwit them at times. The bonus food in this game bounces around the maze, meaning that you have to chase it before it gets away.
Bubble Bobble - Platformer - (bublbobl) - Play as the humans-turned-into-Bubble Dragons, Bub and Bob, as they attempt to rescue their kidnapped girlfriends from the Cave of Monsters. You have to blow bubbles to trap enemies in, and then burst them in order to despatch your foes. Bubble Bobble has an excellent two-player mode, which is actually necessary to play through in order to truly beat the game. And who couldn't love a game where the last boss has a name like Super Drunk?
Asteroids - Space shooter - (asteroid) - A vector-based game where you navigate an unusually-controlled spaceship through a field of asteroids. Shoot a big asteroid, and it will split into two smaller ones. Shoot the two smaller ones, and they will each split into two tiny ones. Beware of the UFOs, especially the small ones, because they can shoot you, too. You can use the Hyperspace button to quickly warp away when you're in a fix, but there is a chance that your ship will explode when it rematerialises, so be wary.
Strider - Platformer - (strider) - Play as the ninja-like Strider Hiryu as he seeks to prevent Grandmaster Meio from taking over the Earth from his space-station, The Third Moon. Excellent soundtrack, and a great challenge.
Burger Time - Platform-esque - (btime) - Help Peter Pepper to construct giant hamburgers (by walking over the individual parts to make them fall to the platform below), whilst avoiding the terrifying anthropomorphic foods that want to stop him. Trap your foes in the burgers for extra points.
Blue's Journey - Platformer - (bjourney) - A solid-enough (and very difficult) platform game, with support for two players simultaneously (you can even carry the other player), and an interesting size-changing ability. Full of cute touches, such as seeing stage enemies happily chatting to each other while you're out of their field of vision. What makes it especially memorable is its incredibly poor translation work, which adds a whole dimension of unintended humour to the game. The game even occasionally misspells the name of its own hero - all hail Bule! (This game is also known as
Raguy.)
Mega Man 2: The Power Fighters - Boss-rush - (megaman2, rckman2j) - The second of the two arcade-exclusive Mega Man games (the first one being Mega Man: The Power Battle). Pick from one of four characters, and fight your way through different sets of classic Mega Man bosses, before attempting to defeat Dr. Wily. You can take the bosses' weapons once you defeat them, and use them against other enemies (think along the lines of Rock, Paper, Scissors). This game has a two-player semi-co-operative mode, where you can help each other to defeat the bosses, but then race to claim their weapon for yourself (the player with the highest score at the end is considered the winner).