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I know they keep the song interesting (like in I Will Always Love You), but what other purpose do modulations serve?

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Modulations are often used in popular and classical music to give some sense of a dramatic narrative. Sometimes this can be "drama" just for the sake of drama, but other times it will actually tell a bit of a story, or just add to the effect of the song.

Take for example "Being for the Benefit of Mr. Kite" by The Beatles (sorry, I can't find a YouTube video of the original). The modulations here move us between C, D, and E minor, in my opinion giving some sense of the disorienting circus tricks that are taking place in the song.

A modulation can also add to the "emotion" of the song (this may be what you meant by 'keeping the song interesting'). Whether or not it's actually a good musical decision, it is rampant in popular music. Here's one particularly awful example, though I'd be happy to hear others' recommendations for worse ones. This is sometimes called "truck-driver tonality" because the key changes sound just like the gears of a truck continuously climbing up in pitch.

Lastly, although I don't have an example for it, I'm curious about the possibility of "associative tonality" in popular music. "Associative tonality," often attributed to Wagner, is when a composer uses a key for a particular character, emotion, or location. I'm on the hunt for popular music groups using this; if anyone knows any, I'd love to hear it!

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    Modulations and key changes seem, to me, to have an effective life of only a bar or two. After that, the listener is involved in the new key, and the old must be forgotten to allow room in the brain for the new. It's a pity that it can't be prolonged, but that's probably the nature of it. Certainly with the 'truck driver's gear-change' - most likely better shorter? – Tim Jun 14 '17 at 16:17
  • Yeah, those modulations are typically "phrase modulations," meaning there's no preparation, and it's just NEW TONIC. But occasionally you'll get a single dominant to prepare you. Certainly not the smooth modulations so common in the common-practice era. – Richard Jun 14 '17 at 16:20
  • +1 for truck-shift! It’s the gears, not the engine, I think... – Bob Broadley Jun 19 at 20:59

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