One can find many instances of classical progressions used in pop/rock songs.
The ubiquitous I-vi-IV-V
光良's 童话 - Listen to the commonplace I-vi-IV-V in the verse section and note how the melodic contour is crafted to intensify the music when this progression is repeated
Likewise, Sting's "Every Breath You Take" opens with a I-vi-IV-V for the intro and verse. Notice the quickening of the harmonic rhyhm towards V? For the first rendition of the verse, do you hear the interrupted cadence at the end?
Eric Clapton's "Tears in Heaven" is also based on this progression in the first half of the verse but uses passing harmonies to create a stepwise descending bass. The second half of the verse is based on a vi-ii7-V7-I circle-of-fifths framework with ii7 being tonicized and vi proceeding to the applied chord with a chromatically descending bassline (V6/vi - V43/IV)
By contrast,
Kitaro's "The Silk Road" starts with a I-vi-IV-I instead of the classical I-vi-IV-V-I? This is followed by a PD expansion before the section ends with an imperfect cadence.
Plagal progressions
Watch Mr Bean "improvise" on the pedal note in "Chariots of Fire" at the London Olympics 2012 and listen to the extended use of neighbour 6/4s as a plagal expansion of the tonic (I-N6/4-I) in the verse followed by a pop-style plagal expansion I-iii-IV-I in the chorus. Notice that the perfect cadence only appears at the end of the chorus.
Non-classical progressions
There are of course progressions that don't follow classical syntax:
I-bVII-bVI(-bVII-I)
LMFAO, "Party-Rock Anthem"
Adele, "Rolling In The Deep"
Bob Dylan, "All Along The Watchtower"
Relevant readings
Gilbert, Steven E. "Reflections on a Few Good Tunes: Linear Progressions and Intervallic Patterns in Popular Song and Jazz." In Music Theory in Concept and Practice, edited by David Beach James Baker, and Jonathan Bernard, 377-92. Rochester: University of Rochester, 1997.