After Burner

After Burner is a series of arcade Flight Simulation Games by Sega's AM2 division.

The games put you into the cockpit of an F-14 Tomcat (or one of two other possible ships in later games). You fly down at high speed destroying waves of enemies with your guns and missiles.

The arcade games are well known for their cabinets. Earlier games in the series can come in standard upright cabinets, but can also come in sit-down motion cabinets in which the seat moves around to correspond to your ship's motions. In the late 80's and early 90's, After Burner cabinets were quite the eye candy.

The series spans five games:

After Burner (Arcade, 1987) The original game, released only in Japan.
After Burner II (Arcade, 1987) More of an upgrade to the original rather than a sequel, After Burner II introduces throttle control for faster gameplay, improved weapon firing, new stages, and revamped music. First AB game to be released outside of Japan.
After Burner III (Sega CD, 1992)
After Burner Climax (Arcade, 2006) Released nearly 20 years after After Burner II, Climax offers brand new graphics, a "Climax Mode" that lets you slow down time to lock on to many enemies at once, two new fighters to choose from, and special "Emergency Order" missions. Later ported in 2010 to Xbox Live Arcade and PlayStation Network.
After Burner: Black Falcon (PlayStation Portable, 2007)

There's also a much lesser-known spinoff called G-LOC: Air Battle, in 1992. It is slower paced than After Burner and puts more emphasis on destroying enemies. Perhaps the only thing anyone remembers about it is that it had a special version designed for the R-360 cabinet, a motion cabinet capable of rolling upside-down.

Tropes used in After Burner include:

Cool Plane: The F-14 in the first few games.
Deadly Walls: In the first two games, there are occasional levels that swap out enemies in favor of walls. Touch one and you lose a life.
Death Is a Slap on The Wrist: For the most part, dying and continuing do not affect your score. However, in Arcades, this eats money.
Excuse Plot: II apparently has you rescuing a Damsel in Distress; it's only mentioned in text at two refuel stops and the ending.
Get Back Here Boss: Every boss in Climax; you are, after all, still tearing up the skies at supersonic speeds.
Hyperspace Arsenal: Your ship starts off with 50 missiles.
Nintendo Hard
One-Hit-Point Wonder: One hit in After Burner or After Burner II and you lose a life.
Point Defenseless: Subverted with the Carrier taking out the missiles with minimal effort and taking only minimal damage to the carrier.
Self-Imposed Challenge: A handful of the EX Options in Climax bring up red text when selected, and their description always begins with "Caution". Among these include turning you back into a One-Hit-Point Wonder and removing your missile recovery, restricting your missile spams to Climax Mode.
Shout-Out: When landing to refuel you land on a runway that looks suspiciously like a road. When you take off again, the chase car is a red Ferrari Testarosa convertible with a hot blonde in the passenger seat.
Spiritual Successor: Sky Target.