It is possible to spawn the Eye of Cthulhu by using a Suspicious Looking Eye.
This item needs to be crafted from 6 lenses. Lenses are occasionally dropped by Demon Eyes (the flying eyes that attack at night along with zombies).
Once you have collected 6 lenses you will need to find a Demon Altar in order to craft the Suspicious Looking Eye. You will probably have to do a bit of searching underground in order to find one of these if you haven't already found one.
Note that in order to summon the Eye of Cthulhu it must be night time. If dawn breaks while fighting the Eye, it will fly away to return the next night with full health.
From 1.1 With Love
Spawn Switching
By using a on/off wire trigger block you can effectively "open" your bed's wall and invalidate the room it's in, leading you to spawn back at the middle of your world. If you're close enough (wiring only works for 2000 blocks or so) you can just hook up a switch at your spawn that'll change the blocks again and allow you to spawn back at your home base. Otherwise, you might be able to coax a contraption with a statue spawner/pressure plate/lava block to toggle it for you automatically.
This post on the TerrariaOnline forums in particular has an interesting bird-based reset circuit that seems to be fairly popular, but you'll need a bird spawner.
Digging the hard way
From your main base, just dig a hole straight down (the classic "Hellevator", if you will). When you get tired of exploring your caves, just start digging left/right towards your shaft. It'll take a while, but you'll at least probably find some goodies (more caves, ores...) on the way, and getting back will be a lot easier. You can even use a depth meter to align all your "escape routes" to the same depth, so that eventually you can just have one long path across the world that speeds up travel.
Previously, on Terraria...
A trick that worked in 1.0.5 was to start up a multiplayer server and explore with a friend (or just explore with two characters locally), then follow the instructions:
- Build a room with a bed. A room isn't necessarily required, but will keep the other person safe. It's best to put the bed in a corner.
- Set your spawn point to the bed.
- Break the bed and use a mirror. Logging out might work but I don't make any promises.
- Do whatever you need at your spawn point. When you're done, let your friend know.
- Put the bed back down in the exact same spot. This is important.
- Use the mirror again.
If you did it properly, you should travel back to where the bed is. This might not work in 1.0.6, though, and it's only good for exploring together -- if either of you get separated, you'll have to travel back manually.
If you're exploring solo, your only real option is just to take the time to improve the path. Wooden platforms over minor gaps and flattening out bumps will help a lot with horizontal movement, and creating a double shaft with a soft landing area (e.g. water) on one side and a wooden platform tower on the other will make vertical travel easier. Using background walls other than dirt will also stop the enemies from spawning.
Best Answer
Build a bed (5 silk, 15 wood), place it and right-click it.
Be sure to place it in valid housing. If correctly done so, you'll see "Spawn point set!".