What are some good/interesting ways to exit a circle of fifths section?

Question

Circle of 5ths is in tons of chord progressions, sounds nice and 'easy', etc. But if you keep going on it the song can sound unreasonably predictable.

What are some good ways to use a little bit of this iii-vi-ii-V-I type thing without it sounding like you're just going round and round and round and round?

EDIT: All the jazz suggestions are cool and probably useful to some other folks (and a bit interesting to me as well) but my main interest is in progressions that lie somewhere on the pop-"avant pop" continuum.

Answer 1

Here are some (partly overlapping) suggestions on how you can vary the sound of a iii-vi-ii-V-I progression:

• Use different additional chord tones (sevenths, extensions, and alterations) for your chords such as flat and augmented 5ths, 6ths, (major and minor) 7ths, (sharp, flat, and regular) 9ths, (sharp and regular) 11ths, (flat or regular) 13ths, and also try added tone chords such as add9 and suspended chords such as sus4. Mix extensions and alterations as you find it sounding okay. (For example you can look for nice melodic voice lines created with the additional chord tones.)
• Mix up what chords are major and minor, utilizing secondary dominants. Ex: III7-VI7-ii7-V7-Imaj7 (i.e E7-A7-Dm7-G7-Cmaj7 in C major).
• Use V9sus4, V11, or IVmaj9/V (i.e. G9sus4, G11, or Fmaj9/G in C major) as the dominant (or similar as secondary dominants).
• End on/resolve to a bVII9(#11) chord (i.e Bb9(#11) in C major) instead of the I.
• End on/resolve to a bIImaj7 chord (i.e Dbmaj7 in C major).
• End on/resolve to a vi chord (i.e Am in C major).
• End on/resolve to IV chord (i.e. F in C major).
• Play the corresponding chords of the relative minor, such as for example I6-#iv7(b5)-vii7-III7-vi (i.e. C6-F#m7(b5)-Bm7-E7-Am), or try out other mediant substitutions for parts of, or for the whole, progression.
• Use slash chords, i.e. use other bass notes than the root of the current chord. Ex: Em7/D-A7/C#-Dm7/C-G7/B-C in C major. (You can also use non chord member notes as you find it pleasing.)
• Use a pedal bass note, for instance a V. Ex: Em7/G-Am7/G-Dm7/G-G7-C6/G in C major.
• Substitute for the dominant only like this: V-V-V-V-I (i.e G-G-G-G-C in C major).
• Use tritone substitutions and chromatic progressions. Ex: ii7-bIII7(#11)-bVI7(#11)-bII7(#11)-Imaj7 (i.e Em7-Eb7(#11)-Ab7(#11)-Db7(#11)-Cmaj7 in C major).
• Use Coltrane changes substitution.
• Play a whole tone ascending progression. Ex: iii7-#iv7b5-bVI7(#11)-bVII7(#11)-Imaj7 (i.e. Em7-F#m7(b5)-Ab7(#11)-Bb7(#11)-Cmaj7 in C major).
• Play a whole tone descending progression. Ex: bVI7-#iv7(b5)-III7-ii9-Imaj7 (i.e. Ab7-F#m7(b5)-E7-Dm9-Cmaj7 in C major).
• Play this wild ascending chromatic progression: III7-IV7-#IV7-V7-Imaj7 (i.e. E7-F7-F#7-G7-Imaj7 in C major). It will, as likely also the whole tone progressions, probably sound way out but might work depending on the context.

Of course you can mix the ideas of the suggestions above to create further variations.
For all of the above you need to pay attention so that your melody notes fit (i.e. don't clash with) the notes of the current chord or chord applicable scale. If they do not fit you'll have to adjust the chord or chord extensions and alterations to fit the melody. For example if the melody uses the ninth scale degree you shouldn't use a sharp or flat nine chord there, or if the melody uses the fifth scale degree you shouldn't use an augmented fifth for the chord there.
And of course you need to use what fits the style of your music - most of the above applies well to jazz but might sound odd in other contexts.

[In case my roman numeral analysis is incorrect, the actual chord in C major denote what I intended for the examples suggestions.]