Gonna have to agree with s4cr1fyc3 on this one: solving the main story case in Under a Killing Moon. I love the Tex Murphy series.

I am really torn between 'Virginia' and 'Her Story' as possible answers but I'm going to go with 'Her Story' as the most memorable. In my humble opinion it's definitely one of the best investigative videogames ever created and it really shows how shaping a narrative relative to its medium can create something very very special. Unfortunately it's not Disco enough, but every gamer, artist, or writer ought to take a look at 'Her Story' nonetheless, Sam Barlow can't get enough credit for producing such a memorable and interesting experience.

Definitely Kathy Rain. I enjoyed that mystery quite a lot!

I really enjoyed the murder mysteries that were in Assassin's Creed Unity, particularly the murder of Jean-Paul Marat.

I wasn't too familiar with the time period when I first played it, so I was unaware of the killer's identity. Following along with the clues was really interesting, and learning about actual historical events was great. I'm glad they also continued this kind of activity in AC Syndicate.

I know it's not much of a detective game despite the fact that the main story revolves around mysterious murders in a small town, but I felt pretty happy when I figured out who the culprit is in persona 4. That moment when everything falls into place and you realize what is the only logical answer, and look back at the journey so far only to see it in a different light, was pretty neat.

Most of the younger users here might not even have heard of that, but back in the days, when it came out, I could not believe how great this game was:

Telariums "Fahrenheit 451"

Close after that we have "Elira - Mistress of the Dark" from Horror Soft

Most modern games I will have forgotten a few weeks after I played them, but these I will bear in my mind forever.

Warning! Some spoilers...

The most memorable criminal case in game for me was case about seeking of serial murderer in Alter ego (2010). At the beginning, the plot of the game is not clear, and the actions are typical for point and click games. We communicate with people, explore the world, collect objects and apply them in the right places. But the final of the game is shocking! We reveal the name of the murderer (a vampire?!), we understand the motives, but we do not have time to complete what we started. One of the main characters is buried alive, and the second goes to prison, where he is severely beaten. The ending of the game shocked me so much that I still remember it after 10 years.

[deleted]

My most memorable crime I got to solve was the blacksmith murder from Ultima VII, just brutal graphics for the time and I loved how the entire plot slowly grew from there. Still one of the most ambitious and interesting game worlds ever.

Since I recently finished Cyberpunk2077, helping certain detective finding his nephew was pretty nerve-wrecking.

apart from that, mysterious The Vanishing of Ethan Carter was just the right length and pleasantly surprised in its denouement.

Solving the murder of a university professor and saving the world along the way in Mean Streets on C64 back in 1989.
I am really looking forward to the full-talkie version of Disco Elysium and hope to get into it soon. Being a grumpy old geezer and all, *#$%* time is not on my side.
(Hey, you! Get off my lawn!)

By far the coolest mystery and coolest story arc that I have even solved in a video game was in the original max payne. Game and the mystery behind the drug know as valkyr. Max Payne, a man who had everything he ever wanted and losing it all to some drug crazed lunatics. Then In the quest for answers and for vengeance practically burning down an entire city to track down and eliminate the evil minds that created the drug that took his family, his whole world. That, coupled with Max Payne’s classic one liners and snarky sarcasm makes that the best mystery I’ve ever solved in a video game.

Solving a case in Phoenix Wright Ace Attorney by cross-examining a parrot comes to mind! "Have I forgotten something Polly?"

My biggest failure and success at solving a crime are related by pure chance. For some reason (wasn't paying attention, missed the clues, who can tell?) I accused the wrong person during the standoff in Borderlands 2 (the one where the robber runs away with the money since that was the outcome in my playthrough, most players experienced a more satisfactory end result I'm sure), so figuring out who the masterminds of the various crimes in Telltale Games' Sam & Max series, particulary the one where you have to follow the trail of the guy/creature/contraption that *spoiler alert* stole Max's brain by asking the right questions, on the first try, was particularly satisfactory to me.

As a person with a bad memory issues I do remember that L.A. Noire was a cool game with some interesting investigations along the story line. But maybe it is just my memory.