Safe-T-Base

Most Safe-T-Bases in Minecraft are in either a cliff, mountain, or underwater. A Safe-T-Base is a base that is extremely safe and is capable of withstanding assault from creepers, zombies, and spiders while still having the capability to gain resources at a rate that is high enough to let someone reach the End of the Game

Cliff
The main advantage of a cliff base is that the base is into a massive cliff with several dozen blocks of ceiling between you and mobs, preferably high enough that any mobs falling off of the cliff will die for easy item collection. The cliff base is also good because you don't need to keep digging down, unlike the mountain base. Unfortunately the cliff base make is much easier for mobs like Creepers and Spiders to reach. Cliff bases are also not very secluded or recessed, making them potentially vulnerable.

Mountain
A mountain base usually consists of a long entrance tunnel to the heart of the mountain (for safety you can reinforce it with two layers of stone), with a protective shield of several blocks consisting of the rest of the mountain around it. The best part about a mountain base is that they are relatively easy to build, while providing good protection. They are secluded enough that they don't suffer frequently from creeper explosions, spiders walking over walls, or skeleton attacks. The downside is that mountain bases dont give you much lee-way in how large your base is, unless you want to run into some caverns. Another disadvantage is that you must gather resources before creating your base, as the mountain is usually surrounded by enemy creeps.

Underwater
The underwater base is the most safe. When you have a base underwater, there are no mobs to contend with. They look cool, with light shining up from the base through the deep waters. They can capitalize on underwater mines, which most miners won't bother with. However, if you want any resources that can't be found in a mine (wood, bacon, leather) it's significantly more difficult, as you must travel away from the safety your base provides to gain them, or if you have enough resources, you could make a tree farm,grain farm and/or mushroom farm which would allow you to stay in your base indefinitely. It is also very difficult to build such bases, due to the high likelihood of drowning during the building process.