Same with Oye Como Va. Santana loves Dorian mode. (I know, it’s originally a Tito Puente tune)
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Similarly, the almost equally iconic “Impressions” (John Coltrane).
Eleanor Rigby is only 2 chords if nobody sings. Do we differentiate between there being 2 chords in just the guitar part vs there being only 2 chords in the finished product?
The vocal line is not usually included when defining chord names, so you should be safe. However, Eleanor Rigby should technically be excluded, because it goes to an Em6 on "All the lonely “PEO-ple”, which does change the flavor of the chord quite a bit.
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Yeah, it’s going to depend where you draw the line on “different chord.” I lump the Em6 in with an Em, personally, like I would consolidate a C-C6-Cmaj7-C6 vamp as essentially one chord, as well. And melody parts can certainly affect what a chord is called in a lead sheet, of course, depending on how prominent the melody note is. That said, the musicologist Alan Pollack calls that Em6 an implied A major chord in context. Cite.. Although he does mention an A minor chord, though I can’t find where in his transcription he’s talking about:
I’m not sure where that A minor is coming from.
But, yes, you can call that Em7-Em6 (or implied A major)-C-E four different chords if you want. I look at it as two chords with a line cliche. It’s gonna depend on your definitions of chords and what notes we’re including. For me, it’s close enough. You can play that song on guitar only playing two chords, if you want. Works for me.
puly, you’re blowing my mind. Theory-geeking all over my two-chord thread. I can’t take you anywhere!! 
Hey! I didn’t start it! I tried to keep it simple, I swear!
Try explaining that to Hank Williams or The Modern Lovers.
And before the nitpickers get to it there is a third chord at the very very very end of “Roadrunner” (the next to last chord right after Jonathan Richman’s “Bye bye!”) there is an E snuck in there. But, dammit, I’ll still call it a two-chord song, although that E-A at the end does truly give a sense of finality, I suppose.
Then you start seeing helicopters.
Agreed, it just depends on how you want to define differing chords. For me, I agree to disagree and think Em6 is worlds different than Em in this context, especially when it’s a descending bassline as it is in Eleanor Rigby. Try to play that chorus (bridge? Whole separate conversation, haha) and just stay on Em, and you don’t really have the same song, do you?
But yes, as OP, WordMan should clarify if he considers 6ths, 7ths, etc. as “different chords”.
I’ve always had a soft spot for “Helen Wheels” by Wings. It’s almost a one chord song. Just romps on the I chord most of the time, moves to the V on the next to the last line of the chorus, then back to the I.
I think in some styles and/or progressions additions to the triad don’t “count” when naming chords, but other times they are clearly vital.
An example off the top of my head is La Vie En Rose. The intitial progression is G/Gmaj7/G6/A-/D7.
Describing those first four measures as G/G/G/A-/D7 would be criminally inaccurate (in my opinion).
(As an aside, anyone want to start a thread in praise of six-word songs? 
)
Watch the sauce, I gotta unload some guns.
Not a two chord song, but I remember being surprised that Harry Nilsson’s Lime in the Coconut is C7 all the way through. A one chord song, yay!
That’s kind of my point; in ER, at the bridge/chorus/whatever, to keep that as Em for three measures would rob us of that descending bassline and therefore disqualify it from being a “two-chord song”. But I’ve been known to be somewhat nitpicky, so maybe it’s just me.
It’s a middle voice there that is descending, not the bassline. The low cello maintains a constant E pedal there. (Not that the distinction takes away from your point.)
To me, it’s all flavors of Em (although I kind of prefer the implied A major interpretation above.) It’s like there’s different types of blue: midnight blue, neon blue, powder blue, prussian blue, etc., and while they’re all distinct, I still consider them variations on the same basic color.
But I totally understand what you’re saying. That descending chromatic inner voice is an important part of the tension and harmony. And I agree. I just choose to think of it as different shades/tints of Em rather than a completely different chord. Like if I see C7 on a lead sheet. I might play C7. I might play C9, I might find C11 or Bb/C fits in there, etc., but it’s all just some flavor of C7 to me.
But I truly didn’t want this to explode into some theoretical side discussion. Let’s just pretend I said Eleanor Rigby is “essentially” just two chords: C and Em, although the Em may come in flavors of Em, Em7, and Em6 (or an implied A/E).