(Copy-paste of my answer on another sub but with more sources added)

Indeed there were! 19th-century Americans generally followed the rule of "if a river is at all navigable, then let's put a steamboat on it". This absolutely included rivers west of the Mississippi.

The Red, Arkansas, and Missouri Rivers (along with many of their smaller tributaries) were all heavily travelled by steamboats throughout the 19th century, especially in the period between 1830-1860. In the 1850's, there were more than 100 steamboats running on the Missouri River alone! The boats on the western rivers at this time wouldn't have been quite as ostentatious as the modern Creole Queen and many of them would have been a decent bit smaller (your average Missouri River boat in the mid-1800s would only have been around 150 ft. long), but they were still an essential part of the United State's expansion west of the Mississippi until being displaced by trains in the decades after the Civil War.

But even after the train became the primary form of transportation, steamboats were still important west of the Mississippi. During the Sioux War of 1876, for example, steamboats were the primary means of logistical support and supply for U.S. Army forces operating up the Missouri and Yellowstone Rivers, and the crew of the steamer Far West were the first to find out about the Battle of the Little Bighorn.

The University of Wisconsin has an extensive collection of historic steamboat photographs, including many of boats on rivers west of the Mississippi, and I highly recommend taking some time to look through it.

https://search.library.wisc.edu/digital/ALaCrosseSteamboat

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Further reading on 19th century American steamboats/river navigation:

Steamboats on the Western Rivers: An Economic and Technological History by Louis C. Hunter

Steamboats and the Rise of the Cotton Kingdom by Robert Gudmestad

From Paddlewheels to Propellers by Charles Fishbaugh

History of American Steam Navigation by John H. Morrison

Way's Packet Directory 1848-1983 by Frederick Way, Jr.

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Edit: This is only about boats on western rivers that are part of the Mississippi River System; there were also paddle steamers operating on rivers in California, the Pacific Northwest, the southwestern US, Alaska, and western Canada throughout the 1800s.