I'm surprised we don't have a thread for this, considering it has much more variety, more frequent releases, and arguably higher quality. Sure, we have to deal with the occasional botched localization and random DSiWare release, but it's generally a nicer place than the Wii U eShop.
I've listed a number of eShop games in the past that I'm quite fond of, some that have delightfully exceeded expectations and others that I think are pretty garbage. So let's share our favorite eShop games, shall we?
Personal essentials-
This is stuff that is pretty much exclusive to the system and fantastic.
Pushmo/Crashmo: Two of the best puzzle platformers on the system, if you have to get only one, don't. Buy both. Okay, go for Crashmo.
Shantae and the Pirate's Curse: One of the most expensive 3DS games or a damn good reason. This is a high quality title and one of the best Zelda-esque titles on the system.
SteamWorld Heist: Amazing strategy game with high replay value and addicting gameplay. Great atmosphere, too.
BoxBoy!: Speaking of great atmosphere, this game has nice, simple graphics and great isolated level mechanics.
Crimson Shroud: THE 3DS RPG, with lovely music, combat, and story. Fairly cheap!
The Keep: The SECOND 3DS RPG, with a high price but great challenge, production values, and combat.
The Starship Damrey: The best adventure game on 3DS, only playable once but truly amazing.
Pokemon Rumble World: nice, simple dungeon crawler with good progression. If you're looking for a slow Streetpass burn, this won't cost you a dime. Full price is 30 dollars, if you're a madman.
Mario and DK: Minis on the Move: hefty lemmings title with a TON of content.
"Might be your Cup of Tea"- these range from absolute personal favorites to satisfying experiences that you should only get if they sound really appealing to you OR if this is the only place you can get them.
Mutant Mudds: No longer exclusive, and still a bit pricey. But the 3D effect on this game is great and it's quite a bang for your buck. One of my favorite platformers.
Mighty Switch Force 1/2: While not exclusive per se, the graphics and switch effect look best on 3DS. MSF2 is absolutely masterful in level design.
Xeodrifter: A quite small, but satisfying Metroid-like. The price for entry is a bit high but it's replayable enough to deserve a spot.
VVVVVV: You can get it cheaper, but it's great on handhelds.
Attack of the Friday Monsters!: Adventure game with card battling mini game, it's chock-full of atmosphere, charm, and a wacky story. You really need to like this genre and Japan to get it.
Liberation Maiden: Crazy mech combat with Kid Icarus: Uprising style controls. Short, but sweet, and an achievement hunting style game.
Iron Combat: War in the Air: Longer and more Japanese than Liberation Maiden, and that's saying something. Mech combat with jet transformations and stat alterations. Come for gameplay, not story.
Gunman Clive 1/2: short, sweet Mega Man-ish action platformers. Dirt cheap, with second game having more problems than the first. However, the unlockable character in both games is amazing.
Fairune: You like Ys Book I and II? Have Ys lite, but with achievement hunting and a badass final boss.
Excave 1/2: Nice loot-based action RPGs, the first being a bit light on content but the second having an absurd postgame.
Moon Chronicles: don't have the original? Now is your chance to enjoy this solid and satisfying portable FPS.
Sakura Samurai: Punch-Out from hell, features money grinding, deteriorating weapons, and movement mechanics. If you enjoy punishing yourself, go for it.
HarmoKnight: The rhythm game on 3DS, featuring a bit of repetitive music but exploration of specific styles. Long campaign, which can be effectively doubled by mastering all 40 levels. Fair warning, mastering this game is really really really hard.
WARNING! These are games I have purchased and haven't found satisfying, or lack in some way. You may still enjoy them.
Azure Striker Gunvolt: Mega Man ripoff from the guys that made Megq Man Zero. Mechanically, it does some interesting things, but it's marred by some poorly-implemented systems. Nothing except the combat stands out.
Mighty Gunvolt: WAS a pack-in with Azure Striker, now a stand alone purchase with DLC. Behold Inafune's Kickstarter abomination in his first appearance as one of three boring characters in a buzz are 8-Bit homage. Again, nothing really stands out.
Kokuga: Remember those guys that made that great shmup Ikaruga? They made this, too! Except it's boring and broken.
Weapon Shop de Omasse: A rhythm game where you make weapons for various archetypes. Dialogue is great, but the gameplay is really dull.
Ironfall: Invasion: Technically impressive and solidly crafted, but a steep price for two halves that are flawed in their own rights. If you want online TPS, get the multiplayer pack and call it a day.
Witch and Hero: Transparently grind-based tower defense game that isn't even worth it's cheap price.
Ninja Battle Heroes: Action platformer with a decent challenge system but lacking really interesting level design and presentation.
Demon King Box: Strategy... tower defense... RPG thing that has really boring mechanics and a terrible localization.
Glory of Generals: Expansive strategy title with a metric ton of content, but a spotty localization that de-emphasizes mission objectives.
PicDun 2: it's a dungeon crawling first person RPG with awful localization. That's important, since there's a text-based puzzle on each floor.