Well I wanted to have a badass Team once during a run-through of Heart Gold. I picked Chikorita (just for the lulz of trading it after catching 2 Ratatta's and 3 HootHoot's alongside it). My boyfriend was round at the time, so I got him breed me a bunch of eggs on his Platinum so I could train an awesome Team all the way from eggs throughout the whole game xD It consisted of Piplup, Ralts, Magby and Shinx (I hadn't trained one in a while), and he also traded me a Master Ball over too. So I'm on my way to get my 5th Badge, and then Raikou jumps out of no where xD So I caught Raikou, and my Team for the playthrough ended up being Empoleon, Gardevoir, Magmortar, Luxray and Raikou! It was an awesome Team (despite having two Electric types haha), but yes I have ditched my Starter.
It's fun to try run through's with different Teams and different Pokémon rare to that Region, I also feel like a badass training Pokémon in Johto before the Elite Four that have never been seen there before xD