Great thread.
I think we almost have to wait a few years to decide this. For instance, judging the 90's in 1999 would be tough - although I would credit Nirvana, Guns and Roses, and Metallica with cleaning out the 80's hair metal bands-thank God. More than anything I see the 90's as unbelievably good alternative rock music....like Blues Traveler, Gin Blossoms, Sugar Ray...honestly way too many to name. Also, when I hear the word "old school rap" I think of the early 90's. I think the 90's also started what has evolved today as modern pop music
For the 2000's.....hard to say like I mentioned above. Seems like rock music has evolved into tons of sub categories that are less listened to like emo (especially in the early 2000's), metal (which has it's own genres), alternative, soft rock, pop rock, etc. And of course country has been very popular. But I think rap, r&b, and pop have largely dominated this decade. As far as artists...I remember Eminem was huge like 6 or 7 years ago, nowadays you don't see him in the news every night. Also there seems to be tons of groups and duos and whatever that have wrote very popular songs but as artists themselves they're nothing huge or largely influential.
Bottom line:
Groups that you will hear on the radio in 20 years from the 2000's
Probably not many, like I said no one was hugely influential or really did anything ground breaking like what we saw in the early 80's and 90's.
Just my opinion.