Sharp Zaurus. I have two (a SL5000D and a C860), they are my pride and joy. They run linux natively and are great pieces of hardware and software. I run the original OS and there are many alternatives. I have a separate page for them.
Agenda VR3. (It's actually a permanent loan from a friend). The hardware is a piece of shit. Underpowered processor, not enough RAM, small grayscale screen, no expansion slots. The saving grace is that / is in flash and it is small. The software is very basic but it is amazing that the developers managed to squeeze an almost usable system in there.
Compaq Ipaq 3600. Better than the agenda but still limited by its hardware. Mine has a sleeve that adds a CF slot, which improves it a lot. Of course it comes with Microsoft PocketPC, but mine currently runs the Familiar/GPE linux distribution. I don't like it very much, lots of things don't work right (package manager, network) and it's quirky to configure, but it's the only linux available.
NEC MobilePro 780. Very nice hardware specs. It's kind of big, but it has an almost full-size keyboard, large screen (but low res), CF and PCMCIA slots. Runs Windows CE 2.11. There is a port of NetBSD for it, but I have so far been unable to install it. The instructions online are confusing. Just found linux for it and will try soon. I've installed a bunch of "linuxy" apps from this guy. They are nice, run well and improve the experience. It needs a better browser though, Pocket IE is crap. I keep it on the living room coffee table for occasional surfing and checking email. It's the perfect size for that.
HP Jornada 680. Nice hardware specs, too, except for the RAM. Smaller than the NEC, it has a usable keyboard, CF and PCMCIA slots in an interesting arrangement. Runs Windows CE 2.11 also. There is a linux port for it that I managed to install without much hassle (look for instructions in the forums). It runs fine and I can go online. I installed Opie and then got rid of it, because it didn't work well. Linux runs from a CF card so it's persistent and it maintains the ability to dual boot to wince, which might come in handy. Lua interpreter compiled for linux on the Jornada. Jim, a small Tcl interpreter compiled for linux on the Jornada.
Sony Mylo. Could be so much better. Wifi works well, browser so-so, Skype works well, keyboard is small but usable. For linux fans, is a big disappointment. The device is locked-up and the linux innards are not accessible.
Here is a list of other PDAs that run linux, that caught my interest. The list is not complete and I know next to nothing about them yet. But if one comes my way cheaply... See a list also here and here.
NEC, Jornada, Zaurus, Ipaq, Zaurus, Agenda.
This page is maintained by Felipe Voloch