Minecraft wiki entry for Defeating_a_Nether_fortress, associated text: You can turn it into a home or base if you like. More details are provided in this excellent guide: Tutorials/Nether Survival. The fortress makes a great base anyway (if you get rid of mobs, see below): huge, looks nice, and ghast-proof walls.
Mobs will quickly turn into a problem if you decide to stay here. The main problems and ghasts, blazes, and wither skeletons. Ghasts are extremely dangerous when they spawn in the fortress itself, often being trapped and killing them usually requires deflecting fireballs back at them. For blazes and wither skeletons, they need a specific light level or lower to spawn: 11 or lower for blazes and 7 or lower for wither skeletons. Note: If you're using cheap light sources like torches, it's remarkably hard to completely flush out blazes. You will almost certainly see them pop up occasionally even if you have high light levels everywhere. Wither Skeleton proofing is easier as each torch gives a wide range in which wither skeletons cannot spawn. Assorting torches or other light sources helps to flush out ghasts as the places they spawn in will now be inaccessible.
These are the only places where you can make blaze farms for blaze rods and experience and wither skeleton farms for skulls. Blaze rods are normally easy and can be made by just remodeling a spawner room (see Tutorials/Blaze Farming), however normally wither skeleton farms (see Tutorials/Wither Skeleton farming) are involved and require lighting up/flattening large parts of your fortress, which makes it not worth it if you only plan to summon the wither once.