I just got to nightmare on my barbarian today. Game is way harder than normal mode. . .I blew through Normal mode easily, and only died a couple times (on the same guy) in act 3 or 4, I forget, to some super enchanted fat guy monster group that killed me in like 2 seconds. But on Nightmare I've died at least half a dozen times and I'm not even done with act 1 yet. Game difficulty really shot up when mode switched.
I also heard Inferno mode is practically impossible, especially with Monk or Barb. Some stuff allegedly does 80k per hit. When you encounter certain combinations of traits on rare monsters (like molten, vampiric, and arcane enchanted or something), they're basically impossible to even kill. :\