Sure - my party was zerging down mobs so fast that the trees didn't even get to spawn their poison plants anywhere except on their corpse, where the graphic is covered up by the actual tree itself. I think 2 people from our party died there.
After that, we occasionally died once as we learned new mob mechanics (bees in act 2, exploding guys in act 3, meteor casters in act 4), but the bosses were dead before they could even cast their abilities (lol at getting all sorts of dodging achievements for mechanics we never saw).
Honestly, I probably had less deaths in Act 1/2 Nightmare than Act 1/2 Normal just because I already knew all of the mob abilities and I had gotten a very good handle on my class (Diamond Skin is winrar as is Illusionist + Teleport spam)..
You can swap Venom Hydra for any other skill (Magic Missile is what I use when I'm not using Venom Hydra) if you don't need to kite or aren't facing any bosses. Just keep up Energy Armor and dump your AP into Arcane Orb. If you're going to be staying in an area for long, drop Venom Hydra. When mobs come up to you, you have several options. You can Teleport out (and VERY far away using Wormhole), you can Diamond Skin and tank it, or you can Wave of Force to knockback and stun.
If you are using a build with like 5 spells that deal damage, you're not going to survive.
I died on the way to the Skeleton King. Nightmare pack haunted me into running right into a wall, at which point they surrounded me.
It was a totally legit death (not a stupid way to die like lag or a bug) and felt awesome!
I still haven't beat normal, but I've died quite a few times, mostly due to high latency issues. My latency doesn't really go below 300ms, and it is commonly 500-700 with spikes over 2000. It sucks when you swing at a barrel and it breaks 20 seconds later (not exaggerating here).
quite alot actually with my barb, then again as soon as i got to hell i thought i couldn't do other then dying
my mage on the other hand blew right through to hell without a single death
Curious. I died quite a bit on normal (Played in a group of 4, for whom I was the "tank") and a few times in Nightmare, but after I reached hell, I've started playing so much more carefully that I've only died once.