I've played all the Digimon games that came out in the US (except for the Savers game, which I never knew existed until recently). From World up to World Championships, if it's Digimon, I've played it. Which means that a little part of me will always hate that I'm just poor enough to never import the rest of the games from Japan. I really want the one for the 3DS and the Adventure anniversary game for the PSP. And the Wonderswan games, but that's really because I'm a fan of Adventure 02 and want to fill in the holes of that messy plotline.
Digimon World DS is my favorite out of the Digimon RPGs for the DS. Main reason is that there's a lot less dialogue to get through, I've found. Dusk/Dawn have a lot of talking going on in them. Dusk/Dawn are still good games, and I love the evolution mechanic in them, where after you evolve a Digimon they return to level one. The encounter rate hurts it, though. It's like every step I take winds up leading to a random battle. But no matter what they're still easier to raise Digimon in than the first World.
The first World game for the PS1 is ridiculous in the amount of managing the player has to do if they want a strong Digimon. There's a Let's Play of the game titled "We're using four strategy guides for this" and it's true. So much manipulating of stats and you didn't really know what stats were required for what evolution. By the time you figured it out, your Digimon dies and you start right back from the beginning. You can get Perfect Digimon if you know what you're doing, but when the game first came out, I was too young to know anything.
Digimon World 2 was my first introduction to dungeon-crawlers. I don't really remember playing this one as much. Probably because I kept restarting to see how the different teams worked out, so I never got far in this one.
For the ones released on the PS1, Digimon World 3 is my favorite. It's more of a standard RPG, though I do have to give credit to Bandai for trying different genres within the same series. This is the one for the PS1 that I got the furthest in, and I'm really upset that my game disc snapped before I could finish it.
As for Digimon World 4, it's there. I tried playing it recently, but didn't get far. It's another shift in genre, and I don't know why I just don't like playing this one.
I do recommend Digimon World DS and Dawn/Dusk. The evolution system is so easy and it's a breeze to get the best Digimon you want. The evolution requirements are shown to you, so you can plan ahead what Digimon you want. They do tend to be a little level-grindy though, but as I said, the encounter rate is so high it's not any trouble to find enemies and if you just press the confirmation button, you can just get through battles without any thought.
The Digimon follow behind you.
The majority of Digimon games have the Digimon following you. World 1, World 3, World DS, Dawn and Dusk... It's a great feature that I enjoy, even though for most of those, it doesn't add much to the game.