Ace Attorney
Nintendo DS - Did You Know Gaming? Feat. NintendoFanFTW
One of the primary Western influences of Ace Attorney is the American crime drama series "Columbo", of which series creator Shu Takumi is a professed fan, and who based his character profiles on the sharpness and secrecy of Lieutenant Columbo:

"I don't touch upon Phoenix's past in the games, and the players don't even know where his parents are. Fans often ask me about the birthdate of a character, or their bloodtype or favorite food, but I don't talk about them on purpose. On the other hand, my own personality might be shining through my characters... In the game, Phoenix's thoughts are shown as monologue, but those inner monologues are just my own, personal thoughts. So when people say "Phoenix is actually quite sarcastic", they're actually talking about me (laugh)."

In the 2015 interview the above quote came from, Takahiro Ookura, writer of the Japanese crime drama series "Enter Lieutenant Fukuie", commented afterwards:

"I can feel the influence of "Columbo" in "Ace Attorney". For example, there's the thing with the IV drops in "Turnabout Succession", episode 4 of "Ace Attorney 4". I won't go into details, but the part where it goes "the only way you can know about this if you were there at that time", that's a type of logic often used in "Columbo"."

Additionally, the character design for Detective Dick Gumshoe is likely modeled off of Columbo's actor Peter Falk; Gumshoe's squint and uneven eyebrows mirror those of Falk, whose signature squint was the result of using an artificial right eyeball stemming from a childhood eye surgery.
For the first three Ace Attorney games, if the game detects the GBA version of the Japanese release of Ace Attorney, Gyakuten Saiban, in the GBA slot while starting the Japanese DS version, the first four cases are unlocked from the beginning. The GBA-slot support was removed from international releases.
Contributed by Mr. Kite
Mia Fey's Japanese given name, "Chihiro", can mean "great depth", or "a thousand fathoms". Shu Takumi describes her name as being a pun, with the kanji together meaning "a thousand questions", as in "If I have to ask him 1000 times, I will!" The second kanji is also the first in "cross examination". The "sato" in her Japanese surname may come from the word for "village" or "home country", while the "aya" part has no particular meaning.
Contributed by SOGESNAKE
Apollo Justice's Japanese surname, "Odoroki", comes from the word for "a surprise".
Contributed by SOGESNAKE
In Edgeworth's original design, he was going to be a 36 year-old veteran prosecutor, but the staff decided that was not interesting enough as a rival. When Shu Takumi saw the second version of the character, he was struck with inspiration and created the back story between him and Wright.
Contributed by SOGESNAKE
Miles Edgeworth's name may come from "edge of a sword", just like his Japanese surname "Mitsurugi", which contains the kanji for sword. This may be a reference to both Gregory and Miles Edgeworth having sharp minds and being "worthy" opponents for Manfred von Karma and Phoenix Wright, respectively. His first name in Japanese, "Reiji" comes from the kanji for "cleverness".
Contributed by SOGESNAKE
Maya Fey's Japanese given name, "Mayoi", means "true evening". When written in kana, "mayoi" means "hesitation" or "doubt". The name was apparently picked from a list of kanji that Shu Takumi liked. "Maya" was chosen as her english name because it closely resembles her Japanese name. The name Maya can either come from the Sanskrit for "illusion" or, similarly to her sister Mia's name, as a pet form of "Maria", which is itself the Latin equivalent of "Mary". "Mary" is originally from the Hebrew for "bitterness". This could be a reference to her sister's unpleasant death. Other possible meanings include: "rebelliousness" and "beloved-child".
Contributed by SOGESNAKE
During production, the name "Souka Naruhodou" (which translates to "Oh, yes, I see now") was suggested as Phoenix Wright's Japanese name, but quickly dismissed. It was decided to settle for just "Naruhodou".
Contributed by SOGESNAKE
In the Japanese versions of each game, Maya Fey's favorite food is ramen. However, this was changed to burgers in the US releases.
Contributed by SOGESNAKE
Sega built a theme park attraction called the "Gyakuten Kenji in Joypolis" dedicated to the Gyakuten Kenji games. The attraction has each visitor investigate a crime scene and look for clues in 20 minutes, after which they then write their conclusions in their own organizers.
Contributed by retrolinkx
Phoenix Wright's Japanese surname, "Naruhodou" is a reference toward the Japanese expression "naruhodo", which roughly means "I see", "I understand" or "indeed".
Contributed by SOGESNAKE
In the French translations of the games, Detective Dick Gumshoe is named "Dick Tektiv", a pun on the word "detective".
Contributed by oshaboy
Shu Takumi, the creator of the Ace Attorney series, had always wanted to make a mystery game. He gained this opportunity when Capcom told him to get 7 inexperienced employees and "make whatever you want". His idea for a lawyer based game was frowned upon by the higher-ups, but tried to convince them that the game would be interesting with its "eccentric" characters.
Contributed by 17thCupOfCoffee
The first 3 games in this series were released on the GBA, only in Japan. When the first game was ported to the Nintendo DS, a new case was added. This case caused a continuity error in the second game, when the original last case of the first game was said to be Edgeworth's last case.
Contributed by RainbowDash256