ANSWER: It is incredibly common in tonal music.
(At least, to me...)
In major keys, the progression is I-IV-viio-iii-vi-ii-V-I. I've went through various examples of this progression in classical music.
For example, the first movement of Mozart's Symphony No. 25 contains the progression I-IV-viio-iii-vi-ii-V7-I in Bb major:
The scherzo of Beethoven's Symphony No. 9, Choral, also has a chord progression in C major that goes like I-IV-viio-iii-vi7-ii43-V-Group-I:
The first movement of Mozart's Piano Sonata No. 16 also has I6-IV-viio6-iii-vi6-ii-V6-I in G major:
I've also found circle of fifths progressions in other genres - for example, anime music. The ED theme of My Neighbor Totoro contains a progression of I-IV-viio-iii7-vi-ii7-V7-I in F major:
The OP theme of Blend S also contains I-IV-viio-iii7-vi-ii9-V-I in the same key:
In minor keys, the progression basically appears as i-iv-VII-III-VI-iio-V-i.
The first movement of Vivaldi's Winter contains F minor i-iv7-VII7-III7-VI7-iiø7-V7-i:
Schubert's Impromptu Op. 90 No. 2 also has an E-flat minor i-iv7-VII7-III7-VI7-iiø7-V7-i:
The Storm from Rossini's William Tell Overture also contains i-iv-VII-III-VI-iio-V-i in E minor:
The finale of Shostakovich's Symphony No. 5 in D minor has a chord progression of i-iv7-VII-III-VI-iio-V-i:
The first movement of Beethoven's Piano Sonata No. 1 in F minor also contains I65-iv-VII65-III-VI65-iio-V65-i progression:
My answer is getting too long, so I guess I'll have to stop here. Anyways, thanks for your question!