Assuming you mean all story quests, if you don't do continue through the story quests you will be unable to access jobs and the associated abilities, certain general abilities for treasure hunting and desythesis, glamours, chocobo training, the beastman vendors, the sightseeing log, some emotes, possibly PVP, as well as most of the content of the game. Also there is a fair chance that if you raise a class to 50 with no job you will get mistaken for a RMT by the community, at they tend to be the only ones who completely abandon the story quests, as opposed to just progressing slowly.