Lasting for only two episodes of the Ninth Doctor's only season, Adam tagged along after his stint as an assistant for artefact collector Henry van Statten ended abruptly along with the lives of his boss and everyone else in Statten's bunker once his most treasured piece, an angry Dalek, broke free and went on a rampage.
After the Doctor saves the day, Rose offered Adam a place in the TARDIS, which he accepted, much to the Doctor's reluctance. Once the TARDIS arrived on Satellite 5 in the year 200,000, it became clear that Adam never really possessed the qualities that much of the other Doctor's companions had. Often whiny and constantly irritating the Doctor, his biggest flaw came in his desire to learn more about the Earth's future by carrying out the incredibly normal procedure of having a hole straight into his brain installed. This then allowed the Jagrafess to read his memories and use his knowledge of the Doctor and the TARDIS to land Rose and the Doctor in some serious trouble.
To be fair, Adam is portrayed incredibly well by actor Bruno Langley, and simple curiosity is what eventually becomes his main downfall. It may have been a bit harsh to leave him on Earth with his brain-hole still operating, but it's unlikely that there are many fans petitioning for the return of Adam Mitchell