Probably not as much as one might think. I'm not an expert, but I have been reading up on the development of the sword. For the medieval age, a viking sword would've been about two or two and a half pounds, and even a big two-handed norman longsword would've only tipped the scale at between three and four pounds. Maybe six for a really big one. The big German GrosseMesser (big knife) was only about four pounds and it was a fairly imposing chunk of steel.
I don't know for sure about all pre-BC era swords, and I haven't studied the Macedonians/Greeks/Romans yet, but I'd be suprised if they weren't similar. The Roman gladius was quite short and light and fast.
Movies like to show big, heavy (10-15lb) monster swords like Conan's but most weren't like that. In actual combat a sword like that would have been slow and cumbersome. A soldier needs something that he could swing repeatedly without exhaustion, and something that would be quick and nimble to handle.
I've done some exercises with a 2.5 lb viking sword... and it's quite a workout. It's the speed that makes the thing. It would challenge anyone to swing one through a series of cuts for more than 15 minutes before your arm feels like its gonna fall off.
Conan the Barbarian is one of my favorite movies. They are in the process of remaking the movie due for a May 2009 release.
Gerald Butler would be my choice for Conan but the producers say that he will be a relative unknown.