Ik on Pikachu's Bulbapedia Page there is a pictuire of a paralyzed Ursaring;
But Thats the Only Time i've seen it. Are abilities in the show often?
Abilities have been shown in the anime, but are usually only used in battles; however, sometimes they have an effect on the plot
Pokemon's abilities that have been activated(linited)
Abilities were shown to work differently in the anime than they would in the games, such as Mold Breaker where it would cancel out any Ability instead of the ones that would prevent the user from using any moves as seen in Shapes of Things to Come! where Cranidos activated it to stop Elekid from activating Static. This was repeated again in O'er the Rampardos We Watched! but this time with Rampardos and Pikachu. Some Abilities were not to shown to be activated at all despite meeting their requirements such as Iron Barbs in Curtain Up, Unova League! when Ferrothorn was hit by Eelektross's Crush Claw, even though it was Ferrothorn's only Ability.
Source
Despite this, in the majority of the anime, abilities don't tend to be shown often compared to the grand total so no, abilities don't appear that often in the anime