Snivy first appeared in BW Snivy Plays Hard To Catch! He took the gangs food and was eating it. Ash was willing to catch him, but he was too fast. Later, Team Rocket find him. He easily back fliped over the Poke Ball. Soon, the gang found him. He battled Tepig, but with a Leaf Tornado he took care of it. After, Ash finds him again. This time, he used Oshawott. Ash told Oshawott to use Attract, but it missed. Then Snivy used Charm, and Oshawott saw Snivy as a hero. Next, with Ash having just a little luck in him, he used Pidove and actually caught him.
Snivy seems to be the most level headed and mature Pokémon currently on Ash's Unova team.
It is suggested that Snivy is one of the few Snivy's who abandoned their previous trainers since they saw the trainer as unworthy or incompetent. Which could explain her high level grass moves and Attract, although it may be possible Snivy was strong before all this.
During Ash and Snivy's first encounter, Snivy displayed surprise at how Ash protected Pikachu and even thought about it a little. This could possibly mean Snivy had some troubled relation with a previous trainer.
Snivy was the only Pokémon on Ash's team to ever defeat Trip's Servine. After Pikachu fell to it, Snivy was able to defeat it. She later fell to Trip's Frillish.
Interestingly, they are both the only female Pokémon currently on the main cast that know Attract.
The two have somewhat opposite personalities; Snivy is calm, collected, mature and willing to fight her own battles no matter how tough her opponent may be, while Emolga is childish, deceptive, lazy and unwilling to battle seriously and/or tricks or forces others to battle for her (by using Volt Switch).
Despite being with Ash all the time in Unova, Snivy has been rarely used in battle, it is possible that Ash only uses her to battle stronger opponents or male Pokémon.
Even though Snivy is a powerful pokemon, she has not been used much by Ash, just like his Palpitoad. She even had her first gym battle against Elesa after being with Ash for some time
Snivy is Ash's second Unova Pokemon confirmed to be female, the first being Unfezant.
Snivy seems to care about Ash's other Pokémon, an example of this was her saving Ash's Tepig in BW079.
Snivy was the the fifth grass-type pokemon to be captured by Ash. First was Bulbasaur, second was Bayleef, third was Sceptile, and fourth was Torterra.
Some how, Ash's Snivy knows how to use Leaf Storm , and it didn't evolved yet . Interestingly, though, she cannot use the Snivy evolutionary chain's signature .