Not to sound like a smart ass but 200 years ago most Americans were farmers, so the commute was simply walking out of the house. 100 Years ago farmers still made up 31% of the labor force.

As far as commuting goes, most people walked to work 100 years ago. Their commute would have been at most 1 mile, most likely shorter. Back then your living area was much more based on where you work rather than where you wanted to live. Think of mill villages and the like. The average person would not have taken streetcars or horse and buggy because it was too expensive.

When streetcars first appear they create what are known as "street car suburbs" where people wealthy enough to take street cars daily would live. They did this to get away from dirty and smelly downtown areas. Keep in mind that street car suburbs were only 2 to 3 miles away from city centers.

The idea of a daily commute over 2 miles is a very mid 20th century phenomenon and closely tied with the rise of cars and suburbanization.

Source: https://www.agclassroom.org/gan/timeline/farmers_land.htm

"Madison Indiana 1811-1860: A Study in the Process of City Building"

Various historic preservation textbooks and an undergraduate class in Urban Geography.

I'm curious how distance for average commutes changed from using horse-drawn carriages to streetcars to cars

I'm not sure that /u/Patriot_Historian's answer for 100 years ago is entirely accurate. By the early 1900s, many large east coast cities like Boston, New York, Philadelphia, and Baltimore had extensive suburbs that stretched up to 5-12 miles from their cities centers. These suburbs were linked to the city centers by a network of commuter rails and street cars, as you describe. I don't think his description of

The idea of a daily commute over 2 miles

as being

a very mid 20th century phenomenon

is entirely accurate, at least for the larger cities on the east coast of the United States.

As early as 1854, we see indications of Houston-style sprawl, as Philadelphia annexes formerly-independent municipalities, shown reasonably well by this map.

By 1890, for instance, Philadelphia was served by a large network of steam-powered commuter railroads that transported people, daily, back and forth from outlying areas up to 12 miles away.

In New York, there were commuter rail lines serving communities on Long Island and in Orange County, by 1880 at the latest.

Sources:

The Divided Metropolis: Social and Spatial Dimensions of Philadelphia, 1800-1975

On the 8:02: An Informal History of Commuting by Rail in America