I was gonna say DS, but I guess it's the 3DS because backwards compatability.

This is the only reason to choose 3DS>DS

I own all the Nintendo handhelds and I love all of them.

Without considering backward compatibility, I would say the best are 3DS and GBA ex-aequo.
GameBoy is close behind even if Pokémon Red/Blue is legendary.

Vita's the only that has ever beaten the contemporary home consoles in the respective generation so I choose that one.

Hardware - Vita

Games Library - DS/PSP

Overall Favourite very difficult for me to choose between PSP and DS. I'll have to give it to DS for Mario Kart DS and Animal Crossing: Wild World. But really they're both a tie for me. Being able to play PSONE games on PSP was fantastic.

I love my 3DS (like the look of N3DS too) but I'll always love my GBA SP blue, it was my first ever handheld I'd bought from the US since at the time of buying it I had no idea it was Nintendo's new design after the GBA, snagged it during my trip to Florida and ended up playing it through most of the holiday with games like DBZ Legacy of Goku, LoZ Oracle of ages etc.

I liked my PSP and the design of the PSP Go but never bought one due to it being digital only and at the time I hated it being a digital only system.

I owned an Original DS but over time I figured I disliked it;s bulky design compared to the SP I owned, eventually came to own a DS lite after a few years.

This question is really hard for me to answer. All my game experiences have been Ninten handheld wise. I saw the Game Gear and the PSP/Vita, but don't have much experiences with them. From the grey brick to the 3DS, I've had great times with them. Mario Land 1 and 2, the RPGs from every handheld of theirs, the first time playing pokemon and loving Silver/Gold so much, The Sonic games from the GBA, the new games possible on the DS, like TWEoY, Rhythm Heaven, and Trauma Center, and the awesome new games on the 3DS. All of them brought me so much joy.

For me to pick just one, well, I'd have to dig through tons of games, and I don't have time to do that... TwT

3DS for its own and the DS library or the DS because it can play Gameboy GameboyColor Gambeboy Advance and Nintendo DS games.

GBA, 3DS/DS Lite are close seconds.

DS is only GBA, the other gameboy games don't work.