The first games that will be playable on a Nintendo DSi and a Nintendo DSi-only will hit later this year, with the first game officially announced to be Alpha Unit's Monster Finder.
As we expect to happen in North America, the first DSi-only game will be from a third party, taking advantage of the handheld's built-in camera as a core gameplay device. Blog AndriaSang points out some of the gameplay details, which features creature collection via the DSi camera, similar in concept to Sony's Invizimals for the PSP.
There's not much in the way of additional details on Monster Finder, which sounds a lot like a Pokemon clone with a title suspiciously close to Capcom's Monster Hunter.
What we do know is that Monster Finder is due to hit Japan this winter (our summer). Expect the same stateside.