How can I safely explore far away from my spawn point?

I keep my bearings by constructing lookout posts. Build them atop hills and within sight of each other. Make each look unique, perhaps by inserting rows of a different block to the rest of the tower. Place torches at the top, and ladders all the way up.

Build a defensible hut around the base of the lookout tower. This hut doubles as a lodge for staying the night far from home base. Place a door from the outside. Monsters can climb ladders, but cannot open doors. You can expand your hut by digging downward into the ground.

You can build roads out of spare cobblestone. This is more cost-effective than minecart tracks.

Well, you could build a minecart system to go to/from your spawn to wherever you want to go. It could get expensive in powered rails though.

Or you could mark the way using torches, large structures, or (if you have a lot of diamond to spare) beacons. Make heavy use of signs.

If you do get lost exploring, building a compass will point you back to your original spawn point.

By far the easiest way is to use portals though, go to the Nether, erect another portal a short distance away, and you will be hundreds of blocks from your original spawn point!

If you are willing to hack you can change your spawn point although there is some speculation of a bed to change your spawn in-game