As with many issues, there are definitely two sides to this question.
NO - you shouldn't re-use screw cap beer bottles because they are made of thinner glass, and there is a greater chance of the bottles breaking or even just the threads breaking and providing a poor seal.
YES - you can use screw top beer bottles. I use them regularly (opened one at dinner tonight), but most of my bottles are crown cap. Also, I live in Canada. Most of our screw top beer bottles are re-used by the breweries, and thus are made of heavier/stronger glass. I have heard of Americans bringing empty beer bottles back from Canada because of this.
No matter what style of beer bottle, you need a capper and new caps. Like Tom said you can't re-use beer caps. I use a bench capper and find that the crown cap bottles seem to be slightly easier to cap. Don't know what the result would be with a hand capper.
What Steve said is true in Canada. In the US the bottles are thinner and not reused. So, good chance of breaking in capping them. If you are in the area where they recycle then (bottles) get the "long necks"