Well, that depends alot on what is needed layout-wise, on the site.
As far as just plain old positioning, I've been doing that for years now. IE 4 could do rudimentary positioning, as well as Netscape 4, but both of those implementations sucked (Netscape4 was REALLY REALLY REALLY bad).
For most "tame" CSS voodoo, IE5+, Netscape 6+, Opera 6+ would be a safe bet for compatibility, and that covers quite a large percentage of the user base usually.
There are some things that are a huge pain in the ass if you try to implement using positioned layers (and NO tables). "Footers" for example. If you want a footer to cling to the bottom of the page, it can get hairy in most browsers (might be an implementation issue).
One little trick that I can offer, that will help you figure out alot of "trick" layouts: Negative margins. Use 'em. They rule.