There are really only two major amusement parks/theme parks in Indiana: Holiday World and Indiana Beach Amusement Resort. That wasn't always the case.
Older Hoosiers may remember Playland Park. The South Bend trolley park opened in the 1890s and closed in 1961. Through the years, it offered coasters such as the Figure 8, the Jack Rabbit, and the Little Dipper. Today, the property is part of Indiana University South Bend.
Other Indiana parks that are no longer open include Rose Island in Charlestown (which was destroyed by the Ohio River flood of 1937), Robison Park in Fort Wayne, Boyd Park in Wabash, and Mounds Park in Anderson. More recently, Fun Spot in Angola offered a petting zoo, a couple of small roller coasters, and some waterslides. It is still standing, but no longer open.
The following are Indiana parks, both big and small, that are operating. They are listed alphabetically.
Columbian Park Zoo
More a zoo than an amusement park, the municipal facility offers some rides such as a small train that adults and kids can ride together. Spinning kiddie rides include helicopters, small boats, and horse and buggies.
Columbia City, Indiana
More a family entertainment center than an amusement park, the center offers go-karts, mini-golf, batting cages, an arcade, and rides such as a Frog Hopper, a Himalaya, and a small Runaway Train junior coaster.
Santa Claus (near the Kentucky border). And yes, you read that right. That's the name of the small town that hosts the park.
Santa reigns dearly (see what I did there?) at his summer hangout, Holiday World, in southern Indiana. In addition to the Christmas theme, the park highlights other holidays and offers the wonderful Splashin' Safari waterpark (included in admission). The park is especially noted for its wonderful coasters, including the huge woodie, The Voyage.
Indiana Beach Amusement Resort
Monticello (in the northwest part of the state)
It's not as big as Holiday World, but the Monticello park has plenty of great rides such as Hoosier Hurricane, Cornball Express, and Lost Coaster of Superstition Mountain, three wooden coasters. The traditional park dates back to 1926. It also offers Indiana Beach Water Park.
Like Columbian Park, this is a zoo first with some great animal exhibits. But it does offer a few amusement rides such as a carousel, the Skyline gondola, a train, and the Kombo family coaster. A 4-D Theater offers animal-themed presentations.
Greenfield and Greenwood (two locations)
Indoor and outdoor family entertainment center with bumper cars, laser tag, and mini-golf.
You should also check out the Abe Martin Louge in Nashville too.