Considering the color, it's actually a Shiny Pidgey and it is very rare like mentioned above. So, it's definitely not a Pokémon you would want to get rid of too fast. Every Pokémon has an alternative form to say that is represented in a different color to themselves. Finding one in HG/SS is about a 1/8000 or so chance since DPPt, so not many people may run into them. This alternate color lists them as a Shiny Pokémon. For instance, if you've heard of the Red Gyarados (which you will encounter as it is part of the game's plot) this is considered to by an example of a Shiny Pokémon.
In HG/SS, if you let it follow you around you will notice that its shiny sprite is also represented, which is quite cool. Seeing as this all sums up your question fairly well, please do use the HG/SS Help Thread next time for anymore questions you may have.
Closed