Was it a response to sales tax? A way to try to undercut competitors?
tl;dr people have theories but no one knows.
RE 1st produce:
Looking at the sources in wikipedia i found a nice academic paper on the subject and followed sources via google that mentioned the papers it cited
http://www.jstor.org/stable/10.1086/429600
Although the true origin of odd pricing is uncertain (Friedman 1967; Dalrymple & Thompsom 1969), the use of odd pricing can be traced back over 100 years (Schindler & Wiman 1989)
and here is a book that goes into the history
looking through stuff referencing these guys seems to support this claim: there are a couple of theories but they don't really involve a major single personal choice as opposed to more general responses such as anti theft, existed along with the post civil war trend of fixed as opposed to haggled prices,
The one thing that seems clear is that it was not in response to a sales tax (though i've seen the claim "odd prices" originate from currency conversions on imported goods)
the aproyphal answer seems to be Melville Stone: a basic summary stolen from wikipedia:
On the March 3, 2008 edition of The Rest of the Story, Paul Harvey, Jr. (substituting for his more famous father) related the story of Stone being responsible for the common use of pennies. The Chicago Daily News was not an initial success, as pennies were not widely used in 1876. According to Harvey, Stone convinced local merchants that employee theft could be reduced if the price of item was sold for 99ยข instead of $1.00 etc., forcing employee to make change for sales and less likely to steal money since it required further calculation. Merchants began experimenting with a penny price drop in their goods, meeting with success among their patrons. An increase in pennies, thought Stone, would help the circulation of his penny paper. When merchants began running low on pennies, Stone purchased several barrels of pennies from the Mint, further increasing their use within the Chicago area
but this doesn't seem correct.
if we ignore the "first" claim, Macy's seems to have played a role in popularizing this when they converted to cash registers around the turn of the 20th century. This seems like the most solid early claim i've been able to find though the "why" people mimiced macy's (and why macys did it) is debatable.
Followup: How does marketing research fit into this picture? Does it actually support that people are more likely to purchase an item even though the price difference is 1 cent?