According to this reddit post, "there are [...] some units that require no maintenance: Cargo Ships, Caravans, and Guided Missiles." Is this true? And are these the only units for which this is true?
Answering the title question: Yes - there are units that do not have a maintenance cost, including caravans, cargo ships, and guided missiles. Answering the in-text question: Yes, it is true that these units do not require maintenance.
well, i just looked thru the coding, and it looks like for some unknown reason, there is only one unit that does not have maintenance.. guided missiles.. oddly other missiles do, but the guided missile entry actually has a line that says nomaintenance true.
"Okay, so what about the Caravans and Cargo Ships?"
The above quoted post is from 9/27/2010. However, these two units were not introduced until the Brave New Worlds expansion, released July 9, 2013. After doing some experimentation, my best ascertainment is that these, too, do not have any maintenance cost. In experimenting, I observed zero alteration in the unit maintenance cost between pre- and post-production of both single and paired* caravans and cargo ships, as well as during the pre- and post-disbanding of said caravans and cargo ships.
*The purpose of building in pairs is in accordance with the "Rule of Evens" described further in the previously cited thread by user DontEatCream.