Who is the final boss of Terraria?

As of version 1.3.0.1, the Moon Lord is the final boss of the game, requiring the defeat of the Golem to begin summoning. It's the last boss in the progression sequence from the Wall of Flesh. The Moon Lord can be summoned by using the Celestial Sigil, or by defeating a number of other enemies and events in the following sequence:

1. Defeat the Cultists that spawn at the Dungeon entrance after beating the Golem.
2. Defeat the Lunatic Cultist.
3. Defeat the four Celestial Towers in the Lunar Events.
4. About one minute after the final Tower is defeated, the Moon Lord will spawn.

If you fail (or succeed) to defeat the Moon Lord, you'll need to begin the process again from the beginning to summon him once more (or use a Celestial Sigil, as mentioned).

The Console and Mobile releases of the game don't currently have the Moon Lord implemented, nor any of the other enemies in the above list. Therefore, in terms of progression, the "final boss" on those platforms would currently be considered the Golem. Both platforms have a unique boss which cannot be encountered in the PC version named Ocram, which is considered to be the hardest boss on those platforms, but it can be summoned as soon as all three mechanical bosses are defeated, and thus can't really be considered the final boss.

Dungeon Guardian is the hardest boss. All damage dealt to Dungeon Guardian is reduced to 1 and he has 9999 HP. He also instantly kills anyone without the maximum armor possible, even then, it only takes one more hit. He also flies and can pass through walls.

http://terraria.gamepedia.com/Dungeon_Guardian

Edit: This question has since been edited to make my answer completely incorrect. Please refer to Mike Kellogg's answer.

The moon lord. Even though the dungeon guardian has a lot of health he isn't a boss and is impossible to kill.