Ash's Fearow was originally a Spearow that Ash encountered on his way to Viridian City, but couldn't capture. Later, when it evolved into a Fearow and was terrorizing Pidgeys and Pidgeottos, Ash attempted to capture it but failed and left his Pidgeot to guard them.
In the manga, Ash captured it early-on, as his Pidgeotto abandoned him early on. It quickly becomes his primary Flying-typePokémon.