In her debut episode Cilan said that Snivy's Moves were very high level, and Snivy evolves into Servine at level 17, and then Servine evolves into Serperior at level 36. Now, I didn't expect Snivy to fully evolve into a Serperior, but she should've at least evolved into a Servine because of her battle experience with Ash, and even before she was with Ash because of Cilan stating Snivy's Moves were very high level. Snivy's Moves are Attract, Leaf Storm, Leaf Blade, and Vine Whip. On Bulbapedia it has the list of Moves a specific Pokemon can learn and at what level. According to Bulbapedia Snivy learns Vine Whip at level 7, Leaf Blade at level 28, Leaf Storm at level 43, and Attract at TM45. I'm not sure if that data applies to the games since I only watch the anime, but Snivy's Moves are very high level and she had lots of battle experience when she traveled with Ash, so in my opinion she should've evolved into a Servine or maybe even a Serperior because of her strength.

I think there are many times when it could of evolved, plus Serperior is my favorite final evolved Unova region starter Pokemon.

I still son't understand how Ash use pokemon like Snivy, I mean if he see that she doesn't evolve why does he keep her in his team? Palpitoad, Boldore, Pignite, Unfenzant and many more pokemon are way stronger than her, and she was used by him all the season.

I chose this because I understand why she didn't evolve in Best Wishes. In one episode, Trip was bragging about how his Servine was better because it had evolved. So Ash was trying to show him that a Pokemon didn't need to evolve to be strong. But yes, I do think she should have evolved later on.

I believe we'll see he again in a later generation, like Ash's Cyndaquil, and it'll evolve then. But if that doesn't happen then she should've evolved during BW.