Ash's Pikachu is where it's at. That pokemon sparked my love for the franchise. So cute!
In the show, it's like that character in all the other shows with the snarky comments, or the amusing intelligence, etc. Just something that draws the audience in, and keeps them watching. How entertaining is it to watch three kids walk around? Meh. (I'm referring to a time before Dawn's Piplup, but you get my point?)
In the game though, I've always found Pikachu kinda.. well, not as great as it seemed. I'm not much on electric types, anyway, but there are better electric pokes out there. I'd be weird to hvae a game without Pikachu, but I'd live just as happy playing it.