How far can you get with a Zoo/Agro Deck?

You can get to rank 8-10 pretty fast with an aggro deck(as you've stated in your question). Beyond that, you're going start slowing down a bit. But I've seen quite a few aggro decks perform pretty well even in Legend rank. Which is sad, because most decks at that level require a lot of thinking/predicting what you're opponent has and can do. With an aggro deck at that level, you just need to play a little more conservatively to avoid board clears.

Warlock and Paladin are both popular choices because they both have good ways to create/maintain a card advantage. Warlock has a much better and more reliable way of doing so with their hero power, but Divine Favor is really quite good in an Aggro deck. As long as you get Divine Favor somewhat early, you can draw 4+ cards with it for 3 mana. For a good comparison, drawing 4 cards would take 8 mana and 8 life for a Warlock.

I'm not a Hearthstone expert, I just noticed that this question hasn't received any answers and thought I'd try to help out!

Everyone thought that the cards unlocked from Naxxramas would make aggro decks less viable, but it has seem to make them even stronger! The deathrattle minions that summon other minions are amazing in aggro decks, and it's not very often that I see an aggro deck without them.

This is more of an update since Malero's answer was submitted before Naxxramas. But yes, Aggro decks are still very strong. I find them boring as hell, but they seem to work and allow you to climb the ladder quickly due to shorter game times.