In my experience, no. It's one of the cruel ironies...you CAN rent music, which you can't do in the US, but CAN'T rent video games. The nice thing about Japan's aversion to used things is that used games and systems (especially REALLY old ones) go for fairly cheap.
I can't find any proper links explaining it but what I've picked up along the way is that renting games is some form of copyright violation in Japan or something along those lines...even the used game market was under threat a few years back when publishers wanted to outlaw that too (look at the back of some Dreamcast titles and you'll a symbol saying "no resale") but were beaten back....With the music CD rentals, retailers and publishers worked out a deal where only items that were a year past their release date could be rented (you'll see a date on the back J music cds) and I believe the rental stores pay a % or overall licence fee back to a music rights clearinghouse as compensation for lost sales.
The Enrichment Center reminds you that the weighted companion cube will never threaten to stab you and, in fact, cannot speak.