Skeletron

Skeletron is the boss that guards a world's dungeon. If one enters the dungeon before killing him the head of the boss will come spinning and growling into the screen, impacting with the player and causing 9999 damage, effectively one-hit killing the intruder. To summon this boss, you must talk to the Old Man at the entrance to the dungeon at night. The man will transform into the Skeletron. If you attempt this at day, he will simply say "Come back at night if you wish to enter" or "I cannot let you enter until you free me of my curse".

Skeletron is a floating, massive skeleton head, with floating arms. What appears to be blood spurting from his arms and neck are most likely "the magic forces holding it together", as noted by Blue in a let's play video.

Skeletron will try to swing his arms at you and has a special attack where he spins his head around and follows a player that should be avoided. His head, at 6000 health points and 12 defense, is the most resilient entity in the game, so it is not a good idea for lower-end players to attempt to defeat him. Destroying the head also destroys any remaining arms that Skeletron has. He must also be defeated before the break of dawn; all players will instantly die if he is still alive at that point.

Once you defeat Skeletron, you may enter the dungeon as many times as you like. You may not battle him again on that map and must create a new one if you wish to fight him.

Currently, if you attempt to enter the dungeon at night without defeating Skeletron, the floating heads that attack you will do only 35 damage like the regular boss. Meaning you could theoretically run into the dungeon and loot a few chests at night if you had potions. If you manage to defeat one (or more) of the Skeletron heads, it will count as defeating the boss, unlocking the dungeon normally.

The old man who stands in front of the dungeon can be killed if you manage to deplete his health, however, if you enter the dungeon Skeletron will instantly spawn and kill you.

If you teleport to your home, Skeletron won't follow you. Also note that if a player fails to defeat Skeletron, Skeletron will instantly die without a "Skeletron has been defeated!" message.

If you build a small house and put a bed inside near skeletron, it is possible to set your spawn point near the boss, making the respawns act as 'extra lives' against him.

As of Update 1.0.4 when you kill Skeletron a Clothier can move into a vacant house.

Drops

 * 5-15 Lesser Healing Potions: 100% (1:1 chance)

Soloing Skeletron
The best way on defeating Skeletron on your own is gaining at least Shadow Armor and a good weapon such as Ball 'O Hurt or Sunfury as they can hit multiple times and has good range, Also using a Star Cannon is an easy way to kill him in under 20 seconds but it uses a lot of fallen stars. The Minishark is also useful against the boss as it is fast and powerful due to its damage per second. Boomerang type weapons are also great for fighting him since they allow for ranged attacks to target his head and don't have a mana requirement or ammunition. Also if you can enter the Dungeon behind Skeletron at night, before the heads get to you, you may be crafty enough that you are able to get into a Chest, maybe obtaining a Handgun. If a Handgun is obtained you can create a Phoenix Blaster, which makes a pretty quick fight with Skeletron.

If you have found a Starfury and have a fair bit of Mana and potions, you could use this very effectively against Skeletron as it can hit all parts multiple times. Jungle Armor would be helpful due to extra Mana regeneration and cost reduction.

When you start the fight it is suggested to get on the roof (which you would have previously flattened) so you have high ground and a lot of space to move, in order to dodge Skeletrons attacks more effectively and avoid or maneuver around any other monsters that may spawn during the fight. Multiple levels of Wood Platforms are recommended, because it allows you to quickly drop down to avoid some attacks. Once on top, you want to target his head because if the head dies the arms die, too. Remember to heal frequently when fighting him, as his attacks can be hard to dodge.

A strategy for lower tier weapons is to use either the War Axe of the Night or The Breaker with Shadow Armor. Both weapons are easier to get early on, especially the War Axe of the Night, since it only requires Demonite Bars. Both weapons allow for holding down the mouse button for a constant swing and a fair amount of damage when combined with Shadow Armor's attack speed increase.

Skeletron's "Final Attack"
Skeletron is the only Boss with what can be called a Final Attack. When the game turns to daylight, Skeletron will charge at the player, inevitably doing 9999 damage to the player nearby, unlike the other 2 bosses, for the Eye of Cthulhu, who just flies away, and the Eater of Worlds, that just doesn't stop fighting until defeated.