On a related note, one thing that changed for me when I started working with a DAW instead of working with musician is that I tend to stick to 4/4 when writing, partly subconsciously I guess.
 
Back in the days, I'd let the drummer figure out a way to write a solid backbeat for my songs. As such, I have songs that I've been wanting to record for years but just can't because I can't play or program those drums parts.
 
Covers are a different story.

Dave Brubeck made a career of wonderfully composed odd time signature songs.

In a more current vein, despie being a world class narcissistic  a-hole, Kanye West has occassionally pulled out a 6/8 rhythm or two. Kind of impressive in a genre so heavily dominated by 4/4.

Rain
Rhythmically, I always preferred the opposite - that is, that any odd time should be integrated so that the average listener doesn't even notice. Most people have no idea what 7/4 is, and yet they all follow through Pink Floyd's Money. To me, that's the ultimate goal.

Not the same TS but Jethro Tull's Living In The Past is another where your non-muso knows not what's going on but can effectively nod along too.

1901 by Phoenix - the verse and chorus are pretty similar but the pre-chorus completely shakes things up.
 
A lot of Vampire Weekend's stuff tends to have rhythms taken from African and Latin sources.

This is nothing new.  Pucinni wrote several of the world's most beloved operas of all time, like La Boheme.  His music usually sounds straightforward and accessible, but if you perform it, you realize just how deeply complex it really is under the surface.  I suspect that rock musicians who do covers of some favorites also discover the unexpected complexity when learning to perform pieces.  Maybe some of the Beatles songs are structurally complex, but they rarely seem so when just casually listening.  And maybe that's exactly what makes a great composer: taking the non-obvious and unexpected and making it seem instantly accessible.

Rain
I dig that stuff. Even something as simplistic as Nirvana's About a Girl which is all Em-G, but then shifts to a C#-F#. Very simple, but it sort of throws you off a bit at first.
 

Nirvana are a great example in general. 
 
Madness had some pretty quirky chord progressions and some quite involved arrangements, considering they were very much a "fun" band. 
 
Here's one: The Kinks, Autumn Almanac. 
 

And who could forget....Queen! Seems like one of the most obvious examples. 
 

Here's another one I always liked, Carrie by Cliff Richard. Fair enough the guy has a reputation of being a sex symbol for the over 70's, but I really like this song. The chords in the chorus have a nice Steely Dan-style twist, always nice to hear some sophisticated harmony in a pop song. 
 

Hi,
 
I don't know music intimately like you folks do, but one of the bands that was best at changing times and still continuing, in my book, was Amon Duul 2. Another band that was very tough on time changes and combinations was Nektar in their best period.
 
I don't see it as a big deal, I just see it as the fact that rock/pop musicians are not advanced enough to play around with other things that have been a part of music history since the beginning of the 20th century. Even Terry Riley, had several things going at the same time, many of them using different time elements, albeit I thought they were mathematically matched to make it easier on the ear. Guru Guru in the early days with Ax Gernrich was also a terrific off the cuff time and such, and Mani Neumeier used to say that he never plays with the bass guitar ... he only plays with and against the guitarist ... and you could see that again when he toured with that Japanese thrash band!
 
I just think that (at times) we're too concerned with intellectualizing something that is not particularly worth discussing within a true/meaningful musical context ... but I will accept that I do not know music as far as you guys do from a playing standpoint!