Eater of Worlds strategy
The Eater of Worlds can be a very tough boss if you're not prepared. A good strategy for tacking this enemy is to take the time to build a large enclosed arena a few dozen blocks above wherever you plan to summon the boss from. This will keep smaller enemies out and the gap will give you enough of a warning to allow you to avoid most of the boss's attacks. Bring a lot of Shurikens if you don't have any flail weapons yet, because they will be able to deal the most consistent ranged damage.
Each randomly generated world comes with at least one floating island. These contain a chest with unique loot and are interlaced with gold and silver ore. Finding a floating island can be tough as the altitude depends on the size of the world you created, but building a "sky bridge" can help. On small worlds, building the bridge at about 200 blocks above sea level will put you within sight of an island. Keep an eye out for vines floating in the middle of the sky, because that's the bottom of your island.
Harvesting fallen stars
Every night time stars fall from the sky. Collecting ten of these lets you increase your maximum mana. On normal terrain this can take a long time and can be a risky proposition in pitch-darkness. By creating a Sky Bridge (by making a ladder about a hundred or so blocks in the air and then laying down stone or dirt in a straight line) you can create a long stretch of easily-traversable land for the stars to land on. With a speed-increasing item such as Hermes Boots or Necro Armor equipped you can travel the length of your bridge collecting stars relatively uninhibited. Zombies will still spawn on the bridge and you might get the occasional harpy or demon eye, but you won't have to contend with rough terrain, chasms, water or anything that spawns from the corruption.
Infinite Life Crystals and Chest Items
Here's a way that you can cheat the system and get as many life crystals and as much stuff out of a chest that you want by using the multiplayer feature.
1. Go to Terraria.org and download their dedicated server program. (Just scroll all the way down at home page)
2. Use it to start one of your worlds or make a new one. (To join your own server, just type "localhost" into the IP address [without quotes]).
3. Search for a life crystal or chest that has something you want to keep getting and save the game through the server command window BEFORE you pick up the item.
4. Pick up the life crystal/chest item and close the server window. You should lose connection In-Game.
5. Re-open your server and join it. You should still have the life crystal/chest item in your inventory.
If you rush back to the spot where you found the stuff, it should still be there. All you need to do is take the item and close the server without saving, and you can just pick up whatever you want over and over again.
Remember to SAVE your progress and make a backup of your save. Alter game files at your own risk. Deposit the item you want in a chest. Save the game and exit. Go back in the game and withdraw the item you want to clone and put it in your inventory. Wait 5 min (very important). Close the game via Alt-F4. Go back into and there is your cloned item. You should now have the same item in the chest and in your inventory.
Each world has an Underground Jungle and a Dungeon. Each of these areas is full of very difficult enemies and very valuable items, and each is found just before the "ocean" at the edge of the world. If you walk in the same direction long enough you will come across one of these. The other one will be at the opposite end. So, if you walk west and find the Underground Jungle, to the east you'll find the Dungeon. It's a really good idea to come with strong armor, plenty of potions and maybe even a friend or two before you try tackling either of these. They can be overwhelming.
Money music box glitched (Fixed in 1.1.1):
This only works in single player. Get a music box and 2 wooden platforms, then place the 2 platforms 2 squares from the roof of your house.Try to place the music box on the platform. The music box will explode into hundreds of boxes. After that, sell the extra for some easy money and free music boxes.