Influence is widespread
Classical music certainly has an influence on many aspects of society. This includes music, movies, poetry, commercials, and culture in general. Many artists, whether they play rock, pop, jazz, hip hop, or other types of music, implement various components of classical music in their work. In a way, every kind of music is related to the music that preceded it. Rock and roll was heavily influenced by blues and country music. It also drew from folk, jazz, and classical.
Much can be learned from the Baroque period
Many rules of music theory were developed during the Baroque period of 1600-1750. This period included composers such as Bach, Handel, and Vivaldi. These rules are just as relevant today as they were back then. Included are theories concerning chords, scales, note patterns, and chord progressions. A lot of musicians learn from these theories, and then implement the knowledge. The modern piano was invented during the Baroque period by Bartolomeo Cristofori of Italy. So anyone playing a piano or listening to piano music is connected to the Baroque period.
Rock musicians utilize classical music
Throughout the decades, many rock and rollers have taken bits and pieces from classical music, and inserted its knowledge and technique into their own style of play. The following artists borrowed from classical music for at least one of their songs. This includes Elvis Presley, The Ventures, The Toys, Procol Harem, The Beatles, Emerson, Lake and Palmer, Neil Diamond, John Denver, Barry Manilow, Eric Carmen, ELO, The Beach Boys, Deep Purple, Billy Joel, Rainbow, Sting , and Green Day, who based their hit "Basket Case" on Pachelbel's Canon in D Major. Relatively new artists such as Alicia Keys are also influenced by classical music.
A big winner in 2012 is classically influenced
Adele Laurie Blue Adkins, better known just as Adele, won six Grammy awards in 2012. This tied the record for most Grammy awards in one night, including the record, song, and album of the year. Classical music was a big influence in the music of Adele. Her 2011 recording "Someone Like You" has definite similarities to the music of Franz Schubert, who was born in 1797. Schubert was an important composer of the era called "The Classical Period". I play the intro to "Someone Like You" on piano. You can hear and feel the classical influence.
Being influenced by classical music
A lot of artists from many genres are influenced by classical music. Being influenced can mean taking a note pattern from Mozart, and incorporating it into your playing style. It could be note for note, or a very similar pattern. It can also mean taking a classical chord progression, and implementing it into your playing or song writing. It can be all or part of the chord progression that is used. The possibilities are virtually endless.
I learned Bach's "Minuet in D Minor" on piano. I was influenced by the wonderful sounding note patterns. Now, when I play certain chord progressions, time permitting, there is a good chance I will play the following note pattern right before an F chord. The note pattern is C # -EGA # -AG- (FE). The notes in parentheses I added myself. Even though I might be playing rock music, I am influenced to a certain degree by classical music. You can become a better player on piano or guitar, by implementing classical note patterns or chord progressions into your own style of playing. I suggest only adding ones you really like. It can work great. A perfect example is Adele.