You've definitely seen them: commemorative state plates featuring landmarks and slogans from a particular state. I call them "state plates," but the official term among collectors is "souvenir state plates." They're often displayed in kitchens, and the designs range from kitschy to classy to impossibly bizarre -- see below for examples of each. According to CountryHome (in their "What's Hot Now" feature!), state plates have been around since the 1870s:
Souvenir state plates date back to the 1870s. When travel became more accessible thanks to cars, they became increasingly popular with jet-setting travelers. There are tons of unsigned, flea-market-type plates out there, but keep your eyes open for some big-name manufacturers, including Vernon Kilns, Homer Laughlin, Salem China Company, and even Wedgwood.
In the post below, I (with the able assistance of Sadie Eck, standing in as Mental_Floss State Plate Research Assistant for this post) have collected plates for ALL FIFTY STATES. I've picked out some favorites first, then the rest are in alphabetical order. Fun things to do while looking through them: count the states you've visited, count the states you've lived in, spot the craziest designs.
South Carolina
New Mexico

Ohio

West Virginia

Oregon

South Dakota

Alaska

Click the little numbers below to see the rest!
Alabama

Arizona

Arkansas

California

Colorado

Connecticut

Delaware

Florida

Georgia

Hawaii

Idaho

Illinois

Indiana

Iowa

Kansas

Kentucky

Louisiana

Maine

Maryland

Massachusetts

Michigan

Minnesota

Mississippi

Missouri

Montana

Nebraska

Nevada

New Hampshire

New Jersey

New York

North Carolina

North Dakota

Oklahoma

Pennsylvania

Rhode Island

Tennessee

Texas

Utah

Vermont

Virginia

Washington

Wisconsin

Wyoming

Acknowledgements
This post is dedicated to Mr. Clinton Bowie, a gentleman and scholar who has dedicated much of his life to the study of State Plates whilst residing in The Beaver State, Oregon. Today also happens to be Mr. Bowie's thirtieth birthday. Happy birthday, Clint!
This post would not have been possible without research assistance by Sadie Eck. Thank you Sadie!
What Did I Leave Out?
Each state has many plates, and often a city or landmark will have its own plate. If you have a favorite plate, leave a link in the comments!
Want to buy a state plate? Tons of these are available on eBay and other places online. I recommend searching for, eg, "oregon state place -license" (to remove license plates from the search).
See also: list of state mottos, list of state slogans, and list of state nicknames.