The 1800s bore witness to many of the events commemorated by US commemorative coins of the classic era - Statehood Centennials, Municipal Anniversaries, the Civil War, National Expansion and Exploration, to name a few. I've split the list into two pieces to make the annotated list a bit easier to digest.
Even still, lots to cover in this post!
1903 Louisiana Purchase Exposition Gold DollarThe 1903
Louisiana Purchase Exposition Gold Dollar were included in an Act "To authorize the Government of the United States to participate in celebrating the one hundredth anniversary of the exploration of the Oregon country by Captains Meriwether Lewis and William Clark in the years eighteen hundred and four, eighteen hundred and five, and eighteen hundred and six, and for other purposes." Among the "other purposes" was "the Secretary of the Treasury shall, upon the request of the Lewis and Clark Centennial and American Pacific Exposition and Oriental Fair Company, cause to be coined at the mints of the United States...gold dollars...to be known as the Lewis and Clark Exposition gold dollar, struck in commemoration of said exposition." The LPE opened on April 30, 1904 and closed on December 1, 1904.
Two types were struck: Thomas Jefferson portrait, and William McKinley portrait.

1904-05 Lewis & Clark Expedition Gold DollarsThe 1904-05
Lewis & Clark Exposition Gold Dollar was authorized in 1902 within an Act "Making appropriations for sundry civil expenses of the Government for the fiscal year ending June thirtieth, nineteen hundred and three, and for other purposes." The Act authorized the Secretary of the Treasury to strike gold dollars "to be known as the Lewis and Clark Exposition gold dollar, struck in commemoration of said exposition." The Lewis & Clark Exposition opened on June 1, 1905 and closed on October 14, 1905.
1918 Illinois Statehood Centennial Half DollarThe 1918
Illinois Statehood Centennial Half Dollar was struck "in commemoration of the one hundredth anniversary of the admission of the State of Illinois into the Union." Illinois was the 21st State to be admitted - on December 3, 1818. The coin was the first US commemorative piece to mark a Statehood anniversary - multiple others would soon follow.
1920 Maine Statehood Centennial Half DollarMaine's Statehood was commemorated in 1920 with the
Maine Statehood Centennial Half Dollar. The 50-cent piece was struck "in commemoration of the one hundredth anniversary of the admission of the State of Maine into the Union." Maine was the 23rd State to be admitted - on March 15, 1820.
1921 Alabama Statehood Centennial Half DollarThe 1921
Alabama Statehood Centennial Half Dollar was struck "in commemoration of the one hundredth anniversary of the admission of the State of Alabama into the Union." The bill was signed into law on the same day as the Maine Statehood coin. Alabama was the 22nd State to be admitted to the Union (ahead of Maine), being admitted on December 14, 1819. Its coin was not struck until 1921, however, due to it not being proposed/approved until 1920 and the US Mint not striking the issue until the second half of 1921.
Two varieties of the coin were struck: Plain and 2x2:

1921 Missouri Statehood Centennial Half DollarThe 1921
Missouri Statehood Centennial Half Dollarwas minted "in commemoration of the one hundredth anniversary of the admission of Missouri into the Union." Missouri was the 24th State to be admitted to the Union, being admitted on August 10, 1821.
Two varieties of the coin were struck: Plain and 2*4:

1922 Ulysses S. Grant Birth Centenary Half DollarThe 1922
Ulysses S. Grant Birth Centenary Half Dollar and Gold Dollar were struck "in commemoration of the centenary of the birth of General Ulysses S. Grant, late President of the United States." Grant was born on April 27, 1822. He rose to the rank of Commanding General of the Union Army during the Civil War and, after the War, served as President of the United States from 1869 to 1877.
Two varieties of each coin were struck: Plain and with Star - for four coins total.


1923 Monroe Doctrine Enunciation Centennial Half DollarThe 1923
Monroe Doctrine Enunciation Centennial Half Dollar was struck "in commemoration of the one hundredth anniversary of the enunciation of the Monroe doctrine." The principles that came to be known as the "Monroe Doctrine" were originally points Monroe delivered in his 1823 State of the Union address to Congress - it was not a standalone document like the Declaration of Independence. The points made by Monroe are generally credited to the pen of his Secretary of State - John Quincy Adams.
1925 California Statehood 75th Anniversary Half DollarThe 1925
California Statehood 75th Anniversary Half Dollar was struck "in commemoration of the seventy-fifth anniversary of the admission of California into the Union." California was the 31st State to be admitted to the Union, doing so on September 9, 1850. California was never an organized territory, it went straight to Statehood. The area was acquired from Mexico in 1848, and was administered by the US military until it became a State.
1925 Fort Vancouver Centennial Half DollarThe 1925
Fort Vancouver Centennial Half Dollar was minted "in commemoration of the one hundredth anniversary of the founding of Fort Vancouver, State of Washington." The fort served as a trading post for the Hudson's Bay Company (HBC) which administered Britain's interests in the area; the area was jointly occupied by British and American frontiersmen, trappers and settlers.

I'll finish up my look at the 1800s anniversaries later in the week.
For other of my posts about commemorative coins and medals, including more about each of the Classic Era US Commemorative Coin presented here, see:
Commems Collection.