1) It was the first time younger people were able to create music for younger people without the filter of older people (management) deciding what got released/heard who's focus was much more to be family friendly and not offend. Most of the 50's and earlier music (with a few notable exceptions... it did start to change with Elvis and a few others in the 50's) had much more of a filter in place. So a lot of the subject matter starting with 60's music is still somewhat timeless as it's a lot of the same stuff every generation deals with and can relate to.
2) Synthesizers started to appear in the 60's enabling some very different sonic options as opposed to the orchestra/big band/4-piece/solo that was typically the limit before then. So it just sounds (a bit) less dated. (i.e. people still like some of the sounds created back then and recreate them today with a twist using more capable synths)
I'm sure there are others, that's just what I came up with...
For example Keith Moon (big Gene Krupa fan) and John Bonham (his triplets and big boomy kick drum sound reminds me to Joe Morello). My exploration of rock leads me to jazz.
Bottom line: cool music is always cool, regardless of the year they were released at