stock build.....extra cooling needed?

So I'm finally building a pc this week. It's my first time and I'm really excited. I was wondering if extra cooling is needed. I'll be running everyting at stock speeds, and will not be overclocking.

Thats totally dependent on what you're buying. But more than likely as long as your case isn't cramped up like a sardine case, and you have at least two case fans you should be fine. If you're going SLI or Crossfire now or in the future you're gonna need more/bigger fans and probably a water cooled system (a small cheap one depending on the cards) would help. But once again at stock speeds maybe not, but still depends on the card. Some run a lot hotter than others.

How would the 5870 do with the haf 922 case? Would you recommend any other case?

That should be perfectly fine. Wish I had a 5870, I plan on getting two of them in a few months. The case has a good bit of room and even if you did change your mind and do a little overclocking it would probably still be okay. Only thing you may want to consider is getting a new fan and heatsink for your CPU. Usually the stock cooling isn't too good when you're running games on max with a high end GPU like the 5870. But that stuff is real cheap only like 30 dollars. Keep in mind though that the issues that come with cooling are usually when your computer is running too hott for too long. Unless you're doing something crazy nothing is ever gonna be destroyed in just a few days from running hot, but high temps for a year or so can trash a vid card or a processor pretty easily.

Well, I've got a 5870 on order and I've got a Antec 300. But I have seen pics of it being squeezed into a 300 so thats ok.