Too Long; Didn't Read
Grand Theft Auto games are set in numerous different universes, dictating their chronology and which games take place after each other. The 2D universe timeline is simple, with the first GTA taking place before GTA 2. The 3D Universe is a little more confusing, with Vice City and San Andreas both occurring before GTA III. And the HD Universe is rife with oddities in its own timeline, with the GTA V prologue occurring before GTA IV - and GTA V itself taking place in between GTA Online's plotlines.
You don't always need to play the games in order, but doing so will help you catch on to important story elements and familiar characters. It's interesting to see how each game connects, and one can't help but wonder who might return for the next title in the franchise.