definitely pokemon- played all the main games and a bunch of the spinoff series like other folks have mentioned. however i bet mario is close, which is funny because i think of myself as a mario hater lol. i literally just don't like the character design, it's not a big deal. but! the gameplay is usually fun so i end up begrudgingly getting into a lot of them and being surprised by how good they are.
I suppose there are some smaller series where I've played all the games but in terms of an actual large number the winner for me is probably Nancy Drew (the HeR Interactive series). Exact numbers are maybe a little fuzzy because some of these I played a very long time ago but I've played at least 18/34.
#6 Secret of the Scarlet Hand
#7 Ghost Dogs of Moon Lake
#8 The Haunted Carousel
#10 The Secret of Shadow Ranch
#11 The Curse of Blackmoor Manor
#13 Last Train to Blue Moon Canyon
#14 Danger by Design
#16 The White Wolf of Icicle Creek
#17 Legend of the Crystal Skull
#18 The Phantom of Venice
#19 The Haunting of Castle Malloy
#20 Ransom of the Seven Ships
#21 Warnings at Waverly Academy
#23 Shadow at the Water's Edge
#24 The Captive Curse
#25 Alibi in Ashes
#27 The Deadly Device
#28 Ghost of Thornton Hall
I would love to play more of the ones I'm missing but sadly these games don't go on sale for super cheap the way they used to (there's been company drama including even firing the voice of Nancy!)
I just want to be a detective
Pokémon for me as well... I've played at least one game from each generation and quite a few spin-offs. I really have no idea what my next most played series would be as I can only think about 3-5 played games for few other titles.