Depends on which generation you're talking about. Could be a Charvel or a Jackson Soloist for some people a little older than me, an SG for some people a little younger than me.If you mean a guitar that is visually identifiable as this generation's instrument of choice, you'd be hard pressed to argue against a PRS.
They exist, in less rabid terms. The Ibanez RG550 80s era guitars with the legendary Edge Bridge is the collector's item of that era. So are the old Charvels and Kramers.Where are the guitars from the 70s, 80s, 90s and now 00s that are as good, if not more, than the '59 Les Paul?
I really don't think that Fender or Gibson (or PRS) covered all the bases. The problem with your restriction to "Popular" guitars is the very reason that we don't have *more* improvements in the genre. Most guitars are a variation on one of those four designs NOT so much because they're the epitome of all things guitar, but because it just made good marketing sense to hope on those bandwagons. The real problem is that manufacturers have so emphasized traditional guitars (and players have so bought into it) that it's difficult for them to implement improvements without being stoned by luddites <G>.Nobody has significantly improved on any of the iconic fifties' designs. Leo Fender and Ted McCarty pretty much covered all the bases, from the rudimentary but musical Telecaster to the difficult-to-make 335, and to date, no one has put in the time and sweat to compete, with the exception of PRS (but his designs borrow a lot from earlier efforts).
If you think that pointy superstrats were the pinnacle of human artistic achievement, you are, of course, allowed to disagree. But seriously, name a POPULAR guitar that isn't a variation on one of those four designs (five, including a late-comer, the SG).
I've owned one of each, except for the Tele, and I can't think of a feature that I'd add to any one of them...unless less weight (for the Les Paul) could be considered a feature.