While the city was platted by Alexander Ralston and Elias Pym Fordham on a 1-square-mile grid next to the White River, the river is too shallow to navigate, making Indianapolis the largest major U.S. city that isn't located on a navigable body of water.

There is some debate about the origin of the city's "Naptown" nickname, but it has been around since at least 1968, when Indianapolis got it's first FM radio station with the call sign WNAP, and the DJs started referring to the city as Naptown (two syllables) which is much easier to say than Indianapolis (six syllables).

The city is perhaps best known for annually hosting the world's largest single-day sporting event: the Indianapolis 500, in which drivers race 200 laps counter-clockwise around the circuit for a distance of 500 miles (800 km).

Louis Meyer requested a glass of buttermilk after winning his second Indy 500 race in 1933. After winning his third title in 1936, he requested another glass but instead received a bottle. He was captured by a photographer in the act of swigging from the bottle, and a local dairy company, recognizing the marketing opportunity, offered a bottle of milk to the winners of all future races. Modern drivers are offered a choice of whole, 2%, and skim.

Elvis Presley performed his last ever concert at the Market Square Arena in Indianapolis on June 26, 1977, for a crowd of 18,000. Bootleg copies of the concert, which have been available on the collector's market for years, prove that Presley's voice was in great shape despite his failing health.

The city has produced many writers, but perhaps the most acclaimed is Kurt Vonnegut, known for his darkly satirical and controversial bestselling novel Slaughterhouse-Five. Upon returning to Indianapolis in 1986, Vonnegut acknowledged the influence the city had on his writings: "All my jokes are Indianapolis. All my attitudes are Indianapolis. My adenoids are Indianapolis. If I ever severed myself from Indianapolis, I would be out of business. What people like about me is Indianapolis."

The Taggart Baking Company of Indianapolis, Indiana, began producing Wonder Bread for a debut on May 21, 1921, following a blind promotion with ads that only stated a "Wonder" was coming on that date. The red, yellow and blue dots on the package represent the balloons Taggart executive Elmer Cline saw while watching a balloon race at the Indianapolis Motor Speedway.

John Dillinger (1903-1934) led a group known as the "Dillinger Gang", which was accused of robbing 24 banks and four police stations. The media ran exaggerated accounts of his bravado and colorful personality and cast him as a Robin Hood. He is buried at Crown Hill Cemetery in Indianapolis, where his gravestone has been replaced several times because of visitors chipping off pieces as souvenirs.

The Slippery Noodle Inn is a large blues bar and restaurant in downtown Indianapolis. It also has the distinction of being the oldest continuously operating bar in the state of Indiana, having opened in 1850 as the Tremont House. The Inn served as a stop on the Underground Railroad during the American Civil War. During prohibition it was called a restaurant, although beer was still being made in the basement, and later it housed a brothel until 1953.

"Take Me Out to the Ball Game", written by Jack Norworth and Indianapolis native Albert Von Tilzer, has become the unofficial anthem of North American baseball, despite the fact that neither of its authors had ever attended a game prior to writing the song. The song's chorus is traditionally sung during the middle of the seventh inning.