No, I didn't get rid of Pikachu. I always grow really attached to my starter (I don't even like to box it temporarily, if I can help it), so I never even considered getting rid of my Pikachu in Yellow. Also, I liked talking to Pikachu, having it follow me, etc., and it would have been a shame to lose access to those features because I traded it away, boxed it, etc.
I think my Yellow Version Pikachu knows Surf (from Stadium), so it's more versatile than the average RBY Pikachu. Of course, its stats are still pretty weak, but for in-game, how much does that really matter, anyway?