Haha, well, I guess Tangrowth is actually my signature Pokémon. It's the only Pokémon I own two of (in separate games) and are trained. I'm particular to my HeartGold Tangrowth though because he is Shiny. He's a Jolly Green Giant! (With a Timid nature...)
I don't REALLY have one, like the pokemon hasn't been in EVERY team, I'd say only about half, but my supposed signature pokemon is shaping up to be Gardevoir. I plan to make a point on having one in future games, at least at the start of them.