What should I bring with me to the Nether [Minecraft]?

Bow and Arrows, to deal with Blazes and Ghasts that will often fly out of reach.
Snowballs also work nicely to injure Blazes and are more rapid-fire than a bow.

Cobblestone to build bridges over lava, or build a ramp/staircase/pillar up to a Nether Fortress (also so you can build a shelter that won't be destroyed by a Ghast's fireballs)
Gravel or sand to let you descend long drops safely

Flint and Steel, to reignite your portal in case a Ghast's fireball hits it and disables it.
Obsidian if you want build a portal close to a Nether Fortress for easier access to Blazes or Wither Skeletons.