Favorite or Infamous? i'll list both:
I had the usual string of Palm Pilots, and such, even a old black and white HP handheld PC, no backlight, couldn't download anything, and ran an ancient and no-longer supported version of CE 1.x. essentially useless. IE no longer worked, and i could barely get email and telnet to do anything...
But the most notable was finding a used (but still old) Apple Newton. i no longer recall which version but it was a huge thing, i think it ran on 4 AA batteries. using the backlight would eat them alive. had Pocket Quicken and some stuff. the most funny part was the horrid handwriting recognition. i think the Simpsons once made fun of it with the 'eat up Martha' line when they tried to type 'Beat Up Martin'. it also lacked app downloads and could do very little on a 56K modem in the day i had it, it was obsolete maybe 5 years before i found the thing. it then ended up in a drawer and i think was lost long ago.
Favorite was my then-new HP Jornada. it had the latest Windows Mobile, looked a bit like XP. i had all sorts of dongles, including the very clunky GPS antenna, voice module and software. as a GPS it reminded me of my old TI 99-4A Home Computer with all the accessories wired to it. worked well though when i flew with my dad on long trips, and it did hold my MP3 collection at the time. it was close to a smartphone then, but smartphones would not exist until a couple more years. if i recall the Motorola RAZR was the latest and greatest toy then