All of the episodes of course! But yes, there's episodes and then there's the ones that actually deal with Conan and his quest to return
to being Kudo Shinichi while alieviating the world of the Black Organization ... Since I've been asked a few times over the years
I thought I'd put this list up as a page... So here's a list of the episodes needed/necessary/critical to understanding the ANIME version
of Meitantei Conan's plot/story regarding Shinichi vs the Black Org and/or intro of main characters and/or developments in
the relationships between characters:
1-5, 10, 11, 18, 27, 28, 32, 34, 35, 42, 43, 48/49 (absolute must), 54, 57/58, 68-70, 76 (enter Kid), 77/78, 81/82 (Minami), 96, 100/101,
116-118, 121/122, 128, 129-131, 134, 136/137, 141/142, 146/147 (Police Love Story #1), 153/154, 156/157 (Police Love Story #2),
162, 166-168, 170-171 (Araide intro), 174, 176-178, 188-193, 199/200, 205/206, 217/218, 219, 220-224, 226/227 (Jodie Santemillion debut),
228/229, 230/231, 233/234, 236/237, 238/239, 241/241, 246/247, 249/250, 253/254, 255/256, 258/259, 263, 264-265 (Eri), 266-268, 269, 271/272,
277/278, 279/280, 284-293, 297-298 (Eri), 299-300, 301/302, 304, 307-311, 316/317, 323/324, 331/332, 333/334, 335/336, 338/339, 340/341,
343/344, 345 (MOST critical to date), 356, 358/359, 361/362, 381/382, 385-387, 390/391, 394-396, 398-399, 400-402, 406-408,
418, 425 (another jaw dropper), 429-430, 431-432, 435-436, 437, 445, 446/447, 449, 457/458, 462-465, 469-470 (Kid),
472-473 (Toichi!!), 474 (Eri), 479 (2hr, Heiji&Hakuba), 484-485, 487 (Police Love Story #8, 1hr special), 489 (Eri),
490 (Shinichi VS Heiji for the 1st time but they didn't know it^^), 491-504, 505-506 (Eri), 507-508 Eisuke knows C is S,
509-511 (Enter Okiya or should we say Bourbon?), 515 (Kaitou Kid) , 516-517 (Heiji & Kazuha),
521-523 Shinichi back and he's a killer, 528-529 Eri solves another murder, 530-531 Satou&Takagi, 534-535 Satou&Takagi,
537-538 Kid, 542-543 Okiya helps solve case, 545-546 bit of Satou's past, 554-555 (Heiji&Kazuha), 558-561 (Detective Koumei intro),
563-564 (Akai (or his twin) lives?), 568-569 (Shiratori's love), 573-574 (Heiji&Kazuha), 579/580/581 (BO, Okiya, "Akai")
583-585 (Shiratori/Kobayashi), 586-587 (Kid), 589-590 (Eri&Kogoro), 592-593 (Ran), 608-609 (all couples affects), 610-613 (Heiji;
"Hound of the Baskervilles"), 616-621 (London case!!), 622-623 (Okiya), 624 (Shiratori/Chiba), 627-628 (Kid) , 646-647 (Sera intro),
648-649 (Sera, Shinichi), ... more and more to come undoubtedly. :)
ie, would ideally want to watch these episodes in order so have a good idea of where the series going ... uum, SUSPECT
of where's it's going ... Aoyama is extremely clever!
And this is *NOT* to say you shouldn't watch all the other episodes (or label them as fillers!!).
The true star of this series has always been the CASES (mysteries) not ANY actual character.
Yeah, yeah, one of these years I'll break it down more as to what was significant in each of these episodes ~_~

Go to Episode List
Meitantei Conan belongs to Gosho Aoyama, Shogakukan, Nihon TV, Yomiuri TV, Toho, Tokyo Movie & TMS