In no particular order:

1. Half minute hero: quirky, quick, hilarious, and a bit stressful at times. It's a perfect mobile title.

2. Disgaea: infinitely scaling/playable strategy rpg. You can power through the game pretty quickly, or take your time and slowly become a god so strong that even friendly healing spells miss you.

3. Patapon (2 and 3): rhythm based game about using drum commands to get your little dudes to complete missions.

4. Dj max (any/all):dance dance revolution for your thumbs. Korean game featuring Korean artists. One of my favorite continuing series.

5. Monster hunter (freedom through portable 3rd): action rpg all about them boss fights. Kill monsters, use their parts to hunt tougher monsters in a game all about incremental progression, inventory management, and learning movement patterns to git gud.

6. Patchwork hero: do you like the dig dug stages where you slice off bits of the land to drop enemies into the water? This is that except they are airships and you must defend your homeland

7. Lumines (1 and 2): musical game about matching colors and making combos in a tetris-esque style game. The devs went on to make tetris effect.

8. Cladun 2: so I heard you like action rpgs, infinite scaling, pixel art, and enough grindy systems that even my power tools get jealous. Enter Cladun.

I'm wondering if I missed any I spent a disproportionate amount of time on.. But these were the first ones to pop into my head.

Edit: I am finally home so I can look over my games... and I definitely forgot a couple.

1. LOCO ROCO! It's a very simple platformer in which you guide your little dudes through stages by using the L and R to tilt the stage. You collect fruits to increase your dude into a larger dude, or several dudes, depending on the situation.

2. N+ Be a platforming Ninja, die a lot.. like a lot a lot. It's.. simple and hard and so satisfying to clear one set of 4 stages at a time. You can even make your own stages if you're feeling up to the challenge.