As mentioned before, I'm still waiting for my next handheld to be announced. I want something with a better-then-320x240 display, wireless networking (802.11b, .11a/g would be nice, bluetooth would be nice), at least a SDIO slot (CF type 2 would be nice), and a built-in keyboard. So, I've been paying more attention then normal to handheld news for the past few months, and I've had a few people ask me where I think things are going over the next year or so.
First, we're going to see a lot of 640x480 screens early in 2004. Toshiba's e800 series is the first PocketPC with a VGA-resolution screen, but very few apps have support for it yet. Sharp's C700-series Zauruses have had VGA screens in Japan for months now, but US models have been limited to 320x240. That's supposed to change in January with the SL-6000. Sony will probably be the first PalmOS vendor with a VGA screen, probably around the time they ship their first PalmOS 6 handheld.
Speaking of PalmOS 6, it's supposed to be released from PalmSource at the end of this year, so we'll probably see handhelds with it start to be announced in March or April. It sounds like this will finally be a real operating system, with multitasking, protected memory, and native ARM applications. PalmOS 5 only runs on ARMs, but it's mostly emulated 68k code. Since current PalmOS devices can't really multitask, background tasks like checking email and RSS feeds turn into a coding nightmare. I tried using a Tungsten C a few months ago in a store, and I just couldn't cope with the delays inherent in switching between mail and web browsing. I really like the basic design of PalmOS, but it hasn't scaled very well so far, and it was never designed to handle removable media or networking. It'll be interesting to see what v6 includes; this is supposed to be the Palm equivalent of MacOS 9 -> OS X or Windows 95 -> NT, so it might be a real contender for me. At the very least, it'll sync with OS X out of the box, unlike PocketPCs (third-party sync tool) or Zaurus (no OS X sync for current handhelds, although they finally released a tool for syncing older models; no iSync).
Later next year, I'd be amazed if we don't start seeing a few high-end handhelds with embedded hard drives, like Cornice's 1.5GB $50 1" model, or something similar from Hitachi. These are similar to CompactFlash-based microdrives, but mounted directly onto the system board of the PDA. If these 1.5-4GB models sell well, then expect 1.8" (iPod) models in early or mid 2005, with up to 80GB of disk space. At that point, it's unclear exactly which market niche they're going for--that's more then enough disk space to be a high-end MP3 player, hold thousands of digital still pictures, and a few hours of digital video. It makes for a seriously bulky handheld, although probably not any worse then Sony's NX/NZ series.
On the feature front, at least half of the over-$300 handhelds on the market should have wireless networking by early next year. Someone, probably Dell, will push that down to $200 or so later in the year. Integrated mini-keyboards will become more popular; right now, HP's 4355 is the only PocketPC with one, although Palm has one and Sony has quite a few (NX/NZ series, TG50, UX series).
It looks like 3D graphics are starting to make inroads; the Toshiba e800 has an ATI video chip with 2 MB of RAM, the Tapwave Zodiac is a PalmOS 5 game machine with its own 3D chip, and the next rev of MS's PocketPC software will have 3D support built in. I'm not sure how useful this is in a pure organizer, but higher-end handhelds have been headed towards mini-PC land for a while now, and once they get networking and larger storage capacities, they're going to start acting a lot more like PCs in a lot of ways.
Two more things: we're going to see: mini-USB host ports on at least a couple high-end handhelds next year. This will let the handheld talk to keyboards, digital cameras, CD burners, mice, printers, and all sorts of things that don't really make a whole lot of sense but will happen anyway. Finally, bluetooth-enabled handhelds are going to get bluetooth keyboard drivers eventually, and someone will start marketing a mini-keyboard with bluetooth.