Been rewatching a few episodes of the 90's X-men cartoon lately, in anticipation of X-men '97 (which I haven't had a chance to watch yet so...no spoilers on this thread please ). And I couldn't help but notice a lot of parallels between the show and the first live-action X-men movie. As in, beyond their merely sharing the same source material, I'm convinced that Bryan Singer actively rewatched the animated series while working on the script, and it informed a lot of his own approach to the universe.
The X-men featured in the film were all prominently featured on the show - Professor X, Cyclops, Jean Grey, Wolverine, Storm, and Rogue. The scene of Rogue kissing Cody and having her powers manifest was in a Season 1 episode of the show, and made it to an early scene in the film. The Scott-Jean-Logan love triangle got quiet a bit of focus on the show, and even more focus in the film.
We're introduced to the world of the X-men in the film from the perspective of Wolverine and Rogue in a very similar manner to how we're introduced to the world of the X-men on the show through Jubilee. In both cases, you have the audience surrogate character attacked by hostile forces (Sabertooth, or the Sentinels), and rescued by the intervention of the X-men. They then wake up in the Mansion's sickbay, wander around the corridors, and end up learning about the Xavier School and the X-men.
Then there's Senator Kelly and the Mutant Registration Act, a major focus of the first season of the show and of the film. Kelly is abducted by Magneto on both the show and the film, though in the latter Magneto succeeds in ultimately killing him (in a way).
A lot of the X-men films were based, to varying degrees, on specific comic story-arcs. X2 on God Loves, Man Kills. The Last Stand on The Cure and the Dark Phoenix Saga. First Class on the 60's X-men comics. Logan on Old Man Logan. And so on. But I think with the first X-men film, the biggest inspiration probably was Season 1 of the 90's X-men cartoon.