You don't need to play them or their spin-offs only on the Xbox 360, that's how.
According to Japanese website Game Data Museum, the top five selling Xbox 360 games are:
1. Star Ocean 4 (Life-to-date: 208,521)
2. Blue Dragon (Life-to-date: 203,740)
3. Tales of Vesperia (Life-to-date: 194,714)
4. Last Remnant (154,493)
5. Resident Evil 5 (121,515)
All of those games, points out Japanese website Hachima Kikou, are available on other platforms or have become available on other platforms. Star Ocean 4 debuted on the Xbox 360, but has recently been announced for the PS3. Blue Dragon was an Xbox 360 exclusive and published by Microsoft, but different versions of the game have appeared on the DS platform, published by Namco and AQ Interactive. The Last Remnant is available on the Xbox 360 and the PC, while Resident Evil 5 is a multi-platform title.
What Hachima Kikou seems to be getting at here is that Japanese gamers who do not own an Xbox 360 or have no intention of doing so can enjoy the Xbox 360's biggest sellers. In short: in the top five, there are no "exclusives" — whatever that term means these days. Though, since Microsoft published the Xbox 360 version of Blue Dragon, that game is very much an exclusive. The franchise, however, does not seem to be as it is being farmed out to other publishers so it can be put on the DS — probably because Microsoft does not have a portable gaming system.
Scrolling through the rest of the top sellers in Japan, though, there do seem to be plenty of definite Xbox 360 exclusives like Viva Piñata, Forza 2 and Halo 3. Gears of War is in the top twenty. So, yes, there are still Xbox 360 exclusives, and those exclusives are selling fairly well in Japan — for Japan. Going by sales figures and looking at this chart, there is enough original first party content to justify a purchase. Maybe it's no longer wise to run out to buy a console, any console, for a third party exclusive title. Can't trust their exclusivity.