I love rock and roll music.  Do you know much about the genre?
It's a genre of popular music that came about in the United States around the late 40s/early 50s, from African American musical styles, like gospel, jump blues, jazz, boggie woogie, and with some country music thrown into the mix!
So it has a lot of influences.  When was rock music the most popular?
Perhaps in the 1950s and mid 1960s, as this was the time when the "more encompassing international style" of rock music came about
Is rock and roll still popular today?  
It's hard to say. However, radio stations have much success playing classic rock and roll, which is a sub genre that usually has one or two electric guitars, a double bass or string bass or electric bass guitar, and a drum kit.
I used to listen to the rock band Rolling Stones.  Are they still around today?
They are! Even though they were formed in 1962 and have had a long list of line-up changes, they're still around today, with Mick Jagger still leading the band.
Wow, that is a long time to be playing music.  I wonder if any other bands have been around that long.
It all depends! You have bands like the Red Hot Chili Peppers who, although have not reached the popularity of the Rolling Stones, have been around since 1983 themselves. Many bands reach a legacy and are able to continue playing for decades