So let's say that it's 2008 and you've achieved your lifelong dream as an employee at Konami, the company that made awesome games like Castlevania, Contra and Gradius. Hooray! Except, you're stuck making garbage portable anime tie-in games instead. Boo! What do you do to pass away the time? Why, you sneak classic Konami minigames in an otherwise completely unrelated title!
There are a few DS games based off of Hayate the Combat Butler. The first one, Boku ga Romeo de Romeo ga Boku de, is a basically a visual novel, where you read lots of dialogue and occasionally interact with the touch screen. It seems pretty banal - except, at the end of each chapter, you can play a minigame, almost all of them just involve hitting objects with the stylus. The goal is to get a high score and increase your "Pathos", which is used for unlocking costumes and other things in the main game. The five minigames are:
Orbs spawn randomly around the screen. Smash as many of them as possible with the style.
Moai heads spit out a bunch of stuff, which also need to be smashed with the stylus.
Based off of the sumo pig boss from the mountain stage of Parodius, this panda trounces back and forth. He stomps on the ground, causing stuff to fall from the sky, which must be smashed with the stylus.
Hit the clouds and juggle the bells.
The most in-depth game, and the only one that doesn't require the stylus (though you can use it), you play a quick game of the Konami puzzle shooter Quarth, where you have to shoot bricks at falling objects, turning them into rectangles and causing them to disappear. The visuals here seem to be taken from the Ganbare Goemon DS title, which included a similar, but more in-depth, Quarth minigame.
If you want to play these, you can just speed through the text in the main game, then hit the Minigame option in the menu. Since they're randomly chosen, you may want to save the game (using the battery save, not the save state), play the game, then reset and reload if you want to try something different. Alternatively, I'm attaching some save states for use with DESMume .9.7.2 which will let you play each of the five games.
Also, if the score tallying sound effect at the end of each game is from the original Castlevania.
Most Tokimeki Memorial games also included unique shooter games - you can read about some of them here.