Phoenix Wright/Apollo Justice/Ace Attorney

The Ace Attorney series of games are really fun! They are mainly focused on the defense attorney Phoenix Wright, and some cases that were important in his "life". The first case in the first game which is called "Phoenix Wright: Ace Attorney" is only about a half hour long, but it helps introduce you to the concept of the game.

Here's an basic overview of what you do (not in any specific order).
1. Search a crime scene
2. Talk to suspects
3. Defend someone in court and look for things in witnesses testimonies (what the saw happen) that don't make sense

It sounds boring, but it's actually really fun!
Here's a demo of the fourth game. It doesn't spoil you really about the other games, but besides this demo, make sure to play the games in order!

PS: The games are rated T, and I've only played two of them, the first and last ones.