I have done extensive research on this topic, and here are the games that I decided to try based on many recommendations:
Lufia Rise of the Sinistrals is what I'm playing now, its a great little action RPG and a real treat if you enjoyed Lufia 2 on the SNES back in the day. It basically has limitless replayability thanks to a New Game+ mode and a randomly generated dungeon called The Ancient Cave. Highly recommended.
Spectrobes is a fun little series that's similar to Pokemon, but in a more action/adventure genre than Pokemon's RPG genre. I'd recommend Beyond the Portals if you're interested.
If you've never played a Harvest Moon game, pick up one of the Rune Factory titles. I know a farming simulator sounds lame, but you will get lost in these games. I have Rune Factory 2 and it's a great little game.
If you're into Tactical games like FFT, pick up Fire Emblem: Shadow Dragon and at least one of the DS Advance Wars games. Those are my favorite to travel with as you can pick up and play them at any point. Of the two I prefer Fire Emblem.
Final Fantasy IV and III should go without saying, but if you're into old school RPGs they're obvious choices.
Scribblenauts is, in my opinion, a must own DS game. Its not particularly deep but its a great distraction when you just need some time to waste.
Finally Animal Crossing: Wild World is loads of fun and another game that you can get lost in if you let yourself. It may seem childish, but its an incredibly deep game.
