It should be pointed out that most of those Mystery Series work because the mystery was acceptably unusual and above the norm for the setting. Agatha Christie's most famous work relied on the killer being unable to leave the social gathering and thus, still among the core group. Sherlock Holmes was a consulting expert that Scotland Yard came to when they were clueless (at the time written, the were among the best at what they did, so if they didn't know, it was a stumper). Similarly, Encyclopedia Brown was a fountain of useless knowledge and most of the cases sent his way already didn't pass the smell test with the client, but the client didn't know what was wrong. Brown's own father, the chief of police, would always be the first client of any book, and it was the benefit of his son's attention to detail and being a fresh pair of eyes, coupled with being a wellspring of factoids that made him the case solver... similarly many neighborhood kids figured something was wrong because of the reputation of the character saying it (Bugs Meanie was doubted because he was the neighborhood bully and Wilford Wiggin's reputation as a Snake Oil Salesman was so well known that Brown not being allowed to watch the pitch would have been a bigger clue that the new scheme was a fraud than anything in the newest pitch).
Modern series tend to look to real life stories for their inspiration. Law and Order typically will source it's plot from a recent headline at time of production, while CSI had career investigators on the writing staff, who were often writing bizzare stories from their own cases OR would find a subculture and plot out a murder based on the subculture's inner drama. They were also fond of the victim's odd death initially looking like it was done by the guy who found the body... only to reveal something else was in play long before they actually died... one memorable episode turned out that the "crime" wasn't a murder, which was staged to gain access for a vault theft, which also wasn't a crime since that was staged to hide an insurance fraud scam (Grissom even pointed out he can't prove the scam to a criminal court beyond reasonable doubt... but the insurance company was well within their right to not pay out on the claim based on the evidence he submitted to them. A Crime mystery with no proven crime.).
Another great way to do Agathe Christie/Holmes is to find a mystery dinner group. Mystery dinners are small parties where the party goers act out a role of a suspect in a game. The game sets out that the players are all suspects in a murder in a closed scene and are give a character sheet with their own character and his/her quirks and witness evidence... like seeing another player-character with the victim before the party, but with another player-character at the time the body was discovered, thus providing an alibi to counter yet another player-character, who notes she didn't see him at the time the body was discovered (two separate players will confirm that that the third was accounted for against the fourth). Depending on how the game was written, the murder will be one of the players, who may or may not be provided the knowledge of his characters role (I've played one where my character was the murderer, but I had no knowledge of it). The non-murders will win if they can sucessfully accuse the player who is the murder, while the murder can win by avoiding any accusations.
The game "Werewolf" uses a similar mystery set up, but here, there are typically three murders (the werewolves) and the remaining players are townspeople. In this set up, each player is secretly assigned a character role that acts and reacts in certain ways and no player is privy to any other players role. The game takes place in rounds, broken into night and day. During the night, the werewolves will silently decide to kill one of the townspeople and the players who are not killed may perform secret actions, and during the day, all players will vote on the person who they believe is a werewolf and if there is a significant majority, they will hang the accused.
Here the game works by ensuring at least one elimination per round (the werewolves always kill, while the townspeople do not need to kill if there is no confidence among them), the werewolves may vote with the townspeople (thus may throw suspicion off of their pact) and each player has a secret role that is typically to the towns benefit, but may cast suspicion on them or ire by the werewolves. For example, one role that is frequently given out is "the child" who is permitted to secretly witness the werewolves but may not publicly accuse anyone during the day out of fear that the werewolves will kill her the next night, but she may vote with the townspeople. If the child can clue in another character about their role, it can cement votes as the child will always vote for a real werewolf and never for an innocent. However the threat is that if a werewolf finds out, they will likely kill her and by not voting if between two innocents, the child might be confused for a werewolf as well. No player is allowed to publically reveal their role, but some players may have an ability to secretly discover another role or do so by looking for patterns (For example, a seer may be able to see one character's role every night and needs to quietly influence to vote to protect innocent characters who are accused, but not alert the wolves, who will target the seer if they figure it out.).
The game is won by the towns people if at any time the entire wolf pack is eliminated and by the wolves if any one wolf surives the final vote (If there are two villagers and a wolf in the final round and the villager is eliminated during the day voting, then the wolfs win (as the remaining villager will die that night). This means that the wolves also have to be wise about their next kill... if they target someone who was never accused of being a wolf, then it narrows the pool of suspicious villagers to be accused. If the wolves leave them, they can later cast doubt on them the next day. There also need not be as many players as available village roles, so each game will be different as not every character is in play (and one died in opening round, though a ref might be sacraficial lamb so the innocent villagers are all given one round to use their skills, and the ref can act as a debate moderator).
This is a great game to play for a mystery writer as it requires players to be stratigic both in what they reveal and what they don't reveal to the crowd writ large as at least one werewolf is present and may target them to eliminate their befits to the villagers.
If you don't have a wide pool of friends, fear not, as these games can be made for single players. While the mystery need not be nefarious (a popular scenario is figuring out Secret Santas) it involves three lists of uniform length and a common relationship between exactly three items on the list. Typically in secret Santa format, it will be a person, a gift that person wants, and a list of Secret Santas (typically a second copy of the first list) and your objective is to find out who got what gift, and who gave it to them. Typically you are given five hints that will eliminate certain combinations. These hints will make a comment most conditions but not all and contain logical operations (Bob did not get the train or the bear). Typically only one complete elimination is made in the hints (Sarah wanted a Book) which can eliminate it for four, and a general rule (Typically, there is only one loop, so Bob can not get Sarah a book if Sarah gave Bob a gift). In secret santa, the player can elimate Bob as his own secret santa.
Another format is Gift Wrap, where five people (Alice, Bob, Charlie, David, Emily) buy five gifts (A book, a train, a bear, a flower, and figurine) and wrap them in five differently patterned wrapping paper (circles, squares, triangles, solid color, stripes) in which case the self referencing becomes harder as all lists are exclusive, and you must figure out which person gifted which toy and what wrapping paper did they use to wrap it.
In either format, the player is still playing detective and wins by making eliminations by the five clues given and the inferences between specific and general clues. The strategy is to take each clue and combine them to make more eliminations (knowing that Alice wrapped her gift in solid color paper and Bob did not give the train of the bear as a gift) will mean we can Bob (and anyone not Alice) from any associations with gifts with solid wrapping. Additionally, we can't yet say Alice's gift is the train or the bear, but if either is her gift, we can elimate the other from associations with Alice (she can't give two gifts), Bob (who didn't use either gift) and solid wrapping paper form an association with Bob (since Alice used it) and from the gifts not used by Alice (since we have her gift).