At first glance this seems especially odd. After all, in many Japanese video stores, you can rent not only Blu-ray's and DVD's but also manga books and music CDs. Most stores even sell blank CDs and DVDs at the checkout counter—just in case you need them for something totally unrelated to the music and movies you just rented.
Games however are only found in two flavors, new and used.
But back in 1983, around the release of the Nintendo Famicon (NES), video games (at this time almost exclusively on computers) were available for rent in most computer stores. However, instead of renting original copies of the games, most stores would bypass the copy protection and make their own bootleg copies to rent out—not to mention also selling that cracking software as well. These rental copies, now sans any and all copy protection were then copied ad infinitum by customers.
Thus in 1984, to stop the rampant piracy, game companies along with the Recording Industry Association of Japan and the Compact Disc & Video Rental Commerce Trade Association of Japan successfully lobbied and changed the Japanese Copyright Act. With this revision, video game rental was de-facto banned in Japan.
I use the word "de-facto" because the actual amendment allows for copyright holders (i.e. game studios) to give permission to rent their games should they choose. It's just that in the last 28 years, few studios have given this permission—though it has happened.
In 1990 SNK leased a special NeoGeo unit to arcades where people paid to play a selection of NeoGeo cartridges. Nearly a decade later, Sega allowed the Dreamcast and its games to be rented in rental chain Tsutaya until the system was discontinued in 2001.
But perhaps the biggest attempt at renting was in 2006 when Koei launched "RentaNet" with two rental stores in the Tokyo metro area. In these stores you could rent games owned by Ideafactory, EA, Sony Computer Entertainment, Taito, Tecmo, Bandai-Namo, Marvelous Entertainment and, of course, Koei. The original plan was to open 1500 stores nation wide by 2008. However, in March 2007 RentaNet was closed down for good.
These days the closest you can come to renting a game is by visiting an internet café. Most of these have game systems to rent and games to play for as long as you are in the store. But, sadly, paying over $5 per hour to sit in the café and play games is hardly more cost efficient than buying them outright.
Will game rental ever be unbanned in Japan? At this point it's anyone's guess. But for now gamers on a budget must resign themselves to buying a game, beating it, and selling it back at about half price.