There are two "official" victory conditions: total conquest or domination (40% of the colonizable planets in the galaxy).
... but as with most Paradox grand strategy games, the real fun is in the journey, not in arriving at the victory conditions. The surprises, successes and failures that you encounter while trying to build an empire are always more interesting (and to me, more fun) than any "Victory!" screen could be.
Set your own goals and try to accomplish them. Some AI-alien jerk cut you off from a valuable star system right at the start of the game? Make it your goal to spend the rest of the game making him pay for that. Colonize star systems in the shape of the Paradox logo. Try to make friends with everybody instead of conquering, then set off an endgame crisis and lead the galactic peace-keeping forces to victory over the Fallen Empire.