Here's one that surprised even me, and one which comes with a little bit of uncertainty that I hope to clear up.
I was, in fact, quite uncertain about this myself when I first started researching it. I have been aware for many years that there was a comic strip called Keeping Up With The Joneses, created by Arthur Momand, that first appeared sometime between 1913 and 1916. The strip revolved around the McGinis family, who were always trying to one-up their wealthy neighbors, the Joneses. The Jones family never appeared in the strip, of course. They were merely referred to by the McGinises constantly, usually in reference to how jealous they would be if they saw what one of the McGinises had purchased or done. According to Momand, this was inspired by his experiences after he moved to New York, and he and his wife's attempts to not be shown up by their wealthy neighbors. He realized how futile it was to do so, and wrote a comic strip to satirize this. The Jones name was, according to him, chosen due to how common it was and how much more interesting it sounded than "Smith." It was never meant to refer to any actual people named Jones.
This is not the story that some people believe. It's the story that they should believe, because it's true, but there are other stories that circulate regarding this phrase that are more convincing to people. I, unfortunately, have previously been one of those people.
The main problem is one of dating. As previously stated, the start date is disputed. Some sources say sometime around 1913, others say 1916. Allan Holtz, author of American Newspaper Comics: An Encyclopedic Reference Guide, and the most trustworthy source I've found, puts the start date at March 31, 1913. This is the date of the earliest published Keeping Up With The Joneses strip that he could find.
This is important, because if the strip started in 1916, there's no way it could be the origin of the phrase. The phrase appears in print outside of the comic strip as early as late 1913 and early 1914. A 1916 start date would suggest the strip had taken its name from the phrase, not the other way around. This discrepancy has caused people to try to find an alternate explanation, and there is one that has become popular. There was a wealthy family who lived in New York in the mid-19th century by the name of Jones, and who had a large mansion overlooking the Hudson river. The family were so wealthy, and keeping up with their wealth would have been so impossible, that people assume the phrase must have been referring to them. This would be a fine assumption to make, if the phrase had appeared in any 19th century publications, which it doesn't.
This was the assumption that I made, however, back when I believed the erroneous sources that gave the 1916 start date. Thankfully, I now know better, and have happily added this phrase to the list of phrases that originated in comic strips.
For more information:
Don Markstein's Toonopedia, about the strip (just don't trust that "First Appeared" date)
The Stripper's Guide, about Arthur Momand
Word Histories, about the phrase