Nintendo launched their DSi remodel of the Nintendo DS in 2009 with a bunch of exclusives sold through an online service (DSiWare) or much more rarely, physically in retail stores in regular DS game packaging. It no longer has the Slot-2 for GBA games, but it came with an integrated new camera that was used extensively in some of the DSiWare releases.
Some late-era normal DS releases also had a DSi mode when played on a DSi, but most of them were still compatible with regular DS units - missing the enhancements of course -. However, besides Pokémon B&W/B&W2, such games were usually shovelware using the DSi camera. The "enhancements" were also a way to region-lock the games, anyways. The quality DSi exclusives were the retail DSi-only Monster Finder and the wealth of digital-only DSiWare software. Examples include, but are not limited to:
- Go Go Koppolo, Shantae
- Rittai Kakushi e Attakoreda ("motion controlled" DSi game with pseudo-3D stereoscopic effect)
- WarioWare Snapped
- Zelda Four Swords 20th Anniversary
Unlike regular Nintendo DS releases, DSiWare software isn't currently emulated by any emulator available. The currently available DSiWare rom dumps are corrupt and missing important data. Most regular "DSi-compatible" retail DS games with a mode for non-DSi models can be emulated in that mode missing the additional enhancements.
There has been some efforts lately by the NO$GBA dev to include it - versions 2.8 onwards include programming paving the way for booting in DSi-mode in the future as well as a dumping utility, but it doesn't boot anything at the moment. DeSmuMe devs are completely uninterested for the moment being in either emulating DSiWare, the DSi camera or multiplayer options.
So far, the only way to play DSi roms or DS roms in DSi mode on real hardware is through the CycloDS iEvolution flashcard. However, the flashcard is now discontinued. Even if you somehow obtain this (expensive) flashcard, the CycloDS iEvolution does not work with the 3DS without patching it's firmware to re-enable the use of DS flashcarts. This flashcard won't let you play any of the digitally-distributed DSiWare software, either.