Here’s a song with what I consider to be simple but high-quality non-diatonic chords:

Let’s start with the chorus, because it’s easier:

Hall & Oates – Kiss On My List (chorus)

Because your [C]kiss, your kiss, is on my list
Because your [Eb]kiss, your kiss, is on my list
Because your [F]kiss is on my list, of the best things in [C]life

This is clearly in C, so it’s I bIII IV I. Something simple I can get behind.

Here’s the verse:

Hall & Oates – Kiss On My List (verse)

My [Cm]friends wonder why I call you all of the time
What can I [Fm]say
I [Ab]don't feel the need
To [Bb]give such secrets a[C]way

This verse seems to start in C minor and end in C major! I think a while ago I wrote something about songs that exist somewhere in between a major key and its relative minor (like the verses of One Headlight, or Just What I Needed), but the verse of Kiss on My List exists somewhere between a major and its parallel minor!

I guess you could say the verse is in Cm, and ends with a Picardy third. But then there would be a key change, and I’m reluctant to call the transition from verse to chorus a key change. Alternatively, you could say the verse is in C, but the C major chord is jarring enough that I’m reluctant to call it the tonic.

I guess harmony is something that defies strict classification.

One could also consider the bIII, bVI, and bVII chords (my favorite ones) as coming from the parallel minor of a major key, so maybe this isn’t as interesting as I first thought. But actually playing the minor i seems less common.

Unfortunately, the instrumental guitar part later in the song is terrible.

Wait, I'm changing my answer because I forgot about the prechorus, which ends in Dm → G → C (start of the chorus). Totally a key change from C minor to C major.

Hall & Oates – Kiss On My List (pre-chorus)

(When they want to) [Fm7]know what the reason [Gm11/D]is
I only [Fm7]smile when alive, and I [Dm11/G]tell them [G]why

Firstly, it's awesome that what you hear in the first 5 seconds of this song ever passed for a professional percussion recording. It's not like Hall & Oates made low-quality recordings; I'm sure that – like many bands in the ‘80s – they had a collective $40,000 of guitars, amps, outboard effects, and main board in the room and spent another $40,000 on personnel time for this song alone, then backed it all up with drums that SOUND WORSE THAN MY TODDLER'S DRUM TOY THAT IS SHAPED LIKE A TUGBOAT. Simpler times.

Re: chorus... you called it C Eb F C. It's subjective, but I'd call it C Cm F C. The bass definitely stays on C. This is relevant because we're going to talk about how much Cm there is in this song.

Because your [C]kiss, your kiss, is on my list
Because your [Cm]kiss, your kiss, is on my list
Because your [F]kiss is on my list, of the best things in [C]life

Re: verse... I agree with your chords (Cm Cm Fm Fm Ab Bb C). It's interesting that a few threads ago, we talked about Home Sweet Home; the verse there is in C, the chorus is Ab Bb C. Someone else who responded to that blog post pointed out that the use of Ab Bb C (bVI bVII I) is really "borrowing the VI and VII from the parallel minor". I really like that assessment, and it is particularly relevant here, since this song is definitely moving between C and Cm, and this makes a clean transition that works in either key.

I think I like Hall & Oates. I saw them once, maybe ~1995. I can't remember if we were seeing them ironically or not. I think Pat Benatar was also playing? Maybe I made that up. Would that make it more or less likely that we were seeing them ironically?

Ah, I was listening without headphones and couldn't hear the bass. And even then, I originally played it as Cm, then decided it was probably Eb6.

So this song is somewhere in between C and Cm, and yet is not bluesy sounding at all. One of my favorite things to do is play other dominant chords as 7#9s, and I can't think of a single place that would sound good here. Maybe the initial Cm in the verse?

Another kind of major/minor ambiguity... I'd say this song is "blues minor" in the verse (i.e., you'd call it E blues, and you hear lots of G and D and no G#), then goes into plain-old-major in the chorus:

Garth Brooks – Papa Loved Mama

(There's no Garth Brooks on YouTube, so I linked to a random cover...)

This example isn't perfect, since the verse sounds more or less like Em A B, and even that Em is really E(blues), if there is such a chord. Like you'd call it E7 even though you *really* wouldn't want me to play the G#. I can't specifically think of another song quite like this, but it feels familiar.

Also, randomly, an unexpected bVI in this song.

[E7 or maybe Em]Papa drove a truck nearly all his life
You know it [A7]drove mama crazy being a trucker's wife
The [B7]part she couldn't handle was the being alone
I guess she [C]needed more to hold than just a [B7]telephone