Speculation ahead! Be aware that I'm letting loose here and you'd be ill-advised to take my wild flights of fancy any more seriously than you would any of the other self-appointed analysts out there. That's not to say there's no factual content here, but please... be discretionary in what you take as gospel.
What's under the DSi's hood?
A good starting question is just what is the DSi? What does it offer? I think it's pretty widely accepted that it represents a minor update in the DS line, though I think there might be more lurking under the surface.
Long-time Nintendo fans may remember the Game Boy Color, and indeed, the DSi has been compared to this system. Game Boy Color brought two things to the venerable Game Boy line: a minor hardware upgrade and a color LCD screen. Many Game Boy titles were enhanced, either explicity or implicitly, for this new system. Some Game Boy Color-specific titles made use of the hardware upgrade to create games not possible on earlier Game Boy hardware, such as the Legend of Zelda: Oracle series—but the system itself wasn't really changed, per se; it was just able to make effectively bigger games with a few new features.
The DSi, I think, takes a slightly different tack. It runs games made for the DS platform, first and foremost. The screens are the same, it has the same number of buttons, and the bottom screen is once again touch-sensitive. The only thing DSi doesn't have is Slot-2, which was typically used for Game Boy Advance games but also allowed Nintendo and others to dabble in Option Paks providing features such as force feedback, extra content, and new interface options.
DSi then adds two key features of which we are certain: dual cameras, and internal/external storage. I believe it's actually a pretty safe bet that either will be available to games or other software that may appear either specifically for or 'enhanced for' DSi down the road. The camera may perhaps be not such a big deal, and outside of the not-terribly-fertile ground for camera-specific games, I don't expect to see it used for DSi-only titles—but it may pop up as an optional enhancement in DS-compatible titles, much like The Legend of Zelda: Link's Awakening DX could use the Game Boy Camera to print in-game 'photos'.
The bigger possibility is storage. DS games currently carry all their storage with them. There's paltry internal storage available on the standard DS platform, and Nintendo's effectively reserved it for storing Wi-Fi Connection settings. If DS software has something to save, it does it onto a special save chip embedded on the DS card itself. These generally range in size from a measly 512 bytes all the way up to 512 KB, though there are exceptions for games like Daigasso! Band Brothers DX, which allows for a full 8 MB of onboard storage. The bigger your storage, though, the more expensive the game gets to manufacture; I'm willing to bet developers have been forced to pare down save features of their game because the publisher doesn't want to front the expense for the pricier save chips.
DSi just might be the ticket for games that have a lot of information to store. Though it's wise of course to moderate one's expectations for Nintendo's well-known conservative attitude toward hardware, it's not unreasonable to expect that DSi will come with at least reasonably-sized internal memory—especially as Iwata himself was speaking to his realization of the pain that Wii's own limited internal flash memory is causing customers and, by extension, the Wii Shop. DSi will debut the DSi Shop, and Nintendo probably realizes that it's wise to make sure that it has enough space to make buying things as painless as possible for its customers; hopefully that includes adequate space, which can then in turn be used by DSi software. There's also the possibility of SD access for even more.
I think there's yet another trick or three up DSi's sleeve that will drive some developers to consider DSi-exclusive titles, though. The DSi Shop will play host to a new web browser, again based on Opera like Wii's Internet Channel and the original Nintendo DS Browser but markedly faster than that original DS effort. (You can see the video for yourself; it's the third box down.) Nintendo president Satoru Iwata speaks of "tuning" making it faster, but I think there's more to it.
First of all, the original Nintendo DS Browser shipped with a memory expansion pak that would slot into Slot-2. This pak, according to reports, more than tripled the available RAM from 4 MB to 14 MB, which this browser required for operation. I doubt that any amount of tuning would make the browser work well with such limited headroom; I predict instead that DSi has a base RAM size that's significantly bigger. [Update: This was confirmed.] DSi-specific software would, of course, be able to take advantage of this. I also suspect, though with less certainty, that the DSi browser's speed is enabled by a processor that can be clocked up from the DS's standard speed on-demand.
Finally, there's one other aspect that might be compelling if you're considering targetting DSi exclusively. Iwata says in his discussion of the browser that "we also achieved faster WiFi communications for Nintendo DSi. When you use the WiFi function of existing Nintendo DS software, the speed does not increase. However, for the software specifically made for Nintendo DSi, it is possible to realize faster communications." Nintendo DS' radio, when speaking Wi-Fi, maxes out at a mere fraction of 802.11's maximum 11 mbps speed. I think Iwata's saying here that DSi's radio will be able to, at the very least, go all the way up to 11 mbps. Either way, there's definitely the possibility to transmit more and faster than on a legacy DS.