Classical music and rock would seem to be worlds apart. After all they have different audiences, different histories and different overall sounds. It doesn't take a trained ear to hear that classical music is much more complex. To some though, similarities can be pointed out that so they can recognize the influence that classical music has had on rock.
The most obvious example of this would be the neo-classical movement of rock that took place in the 80's. Artist like Yngwie Malmsteen composed whole albums of classical-inspired metal. There was characteristic borrowing of composition form such as preludes and suites. Also similar to classical musician’s performance, shows of virtuosity are a staple of the genre. Other guitarists such as Jason Becker performed classical compositions on like "Paganini's 5th caprice" on electric guitar. Yngwie Mamsteen played "Bach's Boree in E minor" as part of his solo. "Flight Of The Bumblebee" was another classical piece covered by a lot of shred guitarists.
There are also more subtle examples. Some bands quote classical music in a recognizable and frequent manner. For example, Deep purple guitarist Ritchie Blackmore quotes classical compositions by tons of different composers, too many to list here. But is you are interested in seeing the whole list you can find it at this link:
Then there are artists that borrow classical progressions and make them barely recognizable. Take modern rockers My chemical Romance whose song "Welcome To The Black Parade" is Pachelbel's "Canon In D". Clarke's "Trumpet Voluntary" is almost made a mockery of by Chumbawuba's humorous hit "Tubthumping".
There were tons of 60's and 70's schmaltzy love rockers like Barry Manilow and Neil Diamond flat out stole classical progressions. I'm not going to get to into that her though because they can't really be considered rock.
In a few cases rock has been fused with classical style arrangements based on those songs. An example of this is Metallica's collaboration with Micahel Kamen performed with the San Francisco Symphony Orchestra. Yngwie Malmsteen wrote the "Concerto Suite For Guitar And Orchestra" for performance with the Philharmonic Orchestra Of Japan. Even Kid Rock fused his trailer park inspired rock with the Detroit Symphony Orchestra.
So next time you hear some rock that sounds like there's a little bit of classical mixed in it is probably because there is. It could be as obvious as a big string section playing in the background or as subtle as a familiar progression engulfed in guitar effects to create a nuance. Recognizing the influence will enhance your overall experience of the music.