My favorite DSi games... I recommend playing on the DSi/XL, because they look terrible on the 3DS.
Zelda: Four Swords. It's not great, but it's free. Go. Now.
Pinball Pulse, which I rebought as soon as it was available on the 3DS because it's just that great. One of my favorite virtual tables.
Trajectile is an awesome arcade/puzzle projectile aiming game. It's a bit difficult to explain, but easy to understand. Probably the game I've sunk the most time into.
X-Scape is a great if frustrating Starfox 2-a-like by the guy behind Argonaut.
Picdun is an awesome and long first-person dungeon crawler crossed with an adventure game and Picross. If you like any of these things, buy it.
Spotto! could be better, but for $2 it's a no brainer.
artstyle:Boxlife is the best of all the artstyle downloadables. You will see 2D surface maps of cubes everywhere for weeks after playing it once you get in the zone.
artstyle

ictobits is very close, though. 8 bit fanservice, awesome music, good mechanics.
artstyle

igidrive is sort of a one-trick pony, but meditative.
Number Battle is a really excellent puzzle fight game. It's really difficult to explain, but I found it very involving.
Paper Airplane Chase and Birds and Beans (i.e. Pyoro 1 and 2) are as good as ever.
Touch Solitaire is solitaire. They could have done more, but it's worth the $2.
Dark Void Zero is an awesome Turrican-a-like, if terribly short.
Maestro's Green Groove is an excerpt of an unreleased-in-the-US rhythm/platform hybrid with classical music. I really like it.
Mario vs DK Minis March Again is worthwhile if you like Lemmings-type games. No Mario involved.
These are pretty much the only games I've bought that I can recommend without reservation.
Shantae, Mighty Flip Champs, and Mighty Milky Way
Do not listen to this man.
Listen to this man. They're not bad at all, but they're overpriced and overrated. Better value can be found elsewhere.
Games I want to like but just can't get into:
artstyle games I didn't list (aquia is broken, base 10 gets tiresome, precipice is frustratingly slow, zengage is good but just didn't keep my attention)
Aura Aura Climber
Go Go Kokopolo
Link n'Launch (awkward controls and mechanics, just didn't like it)
Glow Artisan
Escapee Go (gets incredibly hard a little more than halfway, maybe worth your $2)
Chronos Twins (screens are too far apart to manage them together for me)
A Kappa's Trail (controls are really touchy and it gets too frustrating late in the game)
Games that suck:
Anything using a camera. Not kidding. Please don't waste your money.
Games I'm embarrassed to admit really enjoying:
Escape Trick: Convenience Store (almost intolerably broken, and yet I full-completed it with both endings and all optional actions)
Robot Rescue (shovelware junk production values, awesome gameplay)
Soul of Darkness (Gameloft Castlevania/God of War ripoff)
SMB Alarm Clock (wake up to the invincibility theme! feel like a loser?/!)