The most memorable criminal case I solved has to be the case of the missing bigfoot in Sam and Max Hit the Road. As Sam and Max themselves might put it:

As soon as the quaintly old-timey red phone rang, I knew there was going to be trouble. My kind of trouble.
"Was it a persistently pernicious insurance salesman, Sam?"
"No Max, it was the commissioner! He's sent us on another ridiculous assignment, to find a lost bigfoot of all things."
"Ooh, will it involve needless and hilarious theft and destruction?"
"I sure hope so Max. But there might be clever puzzles and witty dialogue, too."
"As long as they don't interrupt the destruction too much Sam."
"Not with our track record, little buddy."
Yes, this was the kind of case that would take us places, from carnivals to huge balls of twine, to bungee jumping at Mount Rushmore. Just the way we liked it. You can't solve a case like this by normal means. When the facts baffle all reason and logic, the detectives should too. So you don't call the regular police, you call us: an anthropomorphic dog and a hyperkinetic rabbity thing. We're Sam and Max, freelance police.

"Sam, your eloquent detective monologue has activated my impulsive tendencies. Can we do some of that wanton destruction now?"
"We sure can, Max. Let's go."

So, once upon a time I have learned that mysterious menace terrorize some sleepy town in deep old woods. Unfortunately I have arrived too late – fresh bloody trails was all over the place, dead bodies everywhere.
Everyone (who have survived) heaved huge sigh of relief – true hero showed up.

So I, hero, used all my skills to investigate crime scene and track down monster near town – ancient, gigantic, flying horror made of claws and teeth - and killed it eventualy after long and epic battle.

Back in town – I saved them all. A hero that… wait… something was not right, everyone turned hostile. Everyone wanted my head! Is this some crazy cult just born?

When running out of the town from angry mob - I saw him and memories of fight returned to me instantly. Prominent citizen killed by my hand – by accident I swear - that lies nearby to dragon corpse. Dead chicken.

Case closed.

Skyrim.

Due to that Monty Python twist with chicken - I decided to make this outcome canonic for my character. I saved those people but in the end I was that bad guy - Rogue chicken slayer.
Next stop – castle Aaargh. :)

Finding out what actually happened to the Hope in Outer Worlds.

I think one of the best criminal cases solved was the murders of the Beast of Beauclair in The Witcher 3: Blood and Wine.

Well, I'd say that my most memorable criminal case that I ever solved was Whispers of a Machine! In it you need to solve a series of strange murders, but the tools you have to solve them can change based on how you interact with the NPCs; your powers are based on your personality which in turn can feed into the themes of the game and how you can interpret them!

Its an Indie point and click, with this beautiful, semi apocalyptical theme with humanity trying to rebuild from the rubble. The game is kinda short, but there are numerous mechanics that provide some replay value, most distinctive, you get different abilities to solve crimes depending on your actions!
Its a crazy good game and I hope more people come to know about it and play it because its really beautiful, not just visually but with its themes of humanity and our relationships with each other.

I'm a huge fan of detective games or at least games that have me go through a certain thought process that could be in any way related to detective thinking. Mostly a point-&-click adventure fan, I like it when the games make me figure out motives and "perpetrators" by myself, even though, by the very nature of adventure games, more often than not I'm being guided to a specific outcome or answer. I liked the detective process the game took me through in Agatha Christie - The ABC Murders, I really felt they did a good job of putting us in the shoes of Hercule Poirot. Right now I'm playing through Sherlock Homes: Crimes & Punishements, after having finished The Testament of Sherlock Holmes, and I have to say Frogwares did a superb job with the detective process in both those games. My favourites, by far, though, would be the Blackwell series, by Wadjet Eye, even though they're not necessarily "detective games", as the puzzles all revolve around interrogating people, getting to know them, cross-reference hints and dialog options and coming to breakthrough conclusions by ourselves.

I dealt with what was happening in a 15th century monastery beset by the plague, in the IF game Vespers. One of the best games I have ever played. Very hard to forget (if you get to the end, you probably won't ever forget this game).

Monks will die... The plague is inside already... Your world is crumbling. Did I mention that you are the abbot?

If you are interested in interactive fiction (IF) or text games or conversational games of any kind, or even if you have not been before, but you want to live an amazing story, give this jewel a try. It is free, it is all text and it is awesome.

For me was to solve the crimes in Jack the Ripper, from Galilea Studios, as a journalist you must to search who are behind the crimes in New York City. Yeah, they brought to the Big Apple the British criminal. Good songs, and a story that involves the most criminal character of the s. XIX.

The whole mess that was the Snatcher incident, which BTW, would make an amazing rerelease.

Jack the Ripper in its entirety!

The murder of Raymond Maarloeve in Witcher 1. I am not even sure I solved it, actually :)

I'd say the best is the case from the brilliant "Broken Sword: The Shadow of the Templars" – with its absolutely stunning development. From a few (not particularly thrilling) characters in such surroundings and one unusual event, the stream of the plot step by step turns into a rushing river, with dangerous and powerful conspiracy around the world and deep into history. In the end, you love your protagonists and the adventure you've experienced turns out to be much more than you ever expected.

Are all 50 of these codes being given out randomly to those who reply to this thread?

It has been addressed here:
https://www.gog.com/forum/general/how_not_to_make_a_corporate_giveaway/post33

"As for picking people randomly, the local laws of Poland, where our company is based, prevent us from organizing random raffles of any kind. These are considered gambling and that’s why we make sure to have a jury."

Witcher 1. The quest is quite elaborate and you need to carry out an autopsy for example, and at some point it turns out there is a big surprise with your "partner". We also get to work together with the lovely Shani, which is a bonus in itself. It's one of my best memories from the original Witcher, which is saying a lot.