I've posted before on talk.bizarre how I've got a passion for music with odd time signatures, where odd means "abnormal", although a good measure of abnormality is that the topmost number in the meter is not even (except if it's 3; technically, you just get the prime factors from the top number, and if any are larger than 3, it's odd).

I'm so aware of time signature stuff that I can, without reference to anything, trivially sort the performers I listen to into clumps, depending on whether or not I own at least one song of theirs in an odd time signature (normally, but not this time, I count dropped beats as odd times as well, e.g. a single measure of 3/4 in a 4/4 song).

some very incomplete lists of "rock" music in odd times

Performers who aren't/weren't afraid of odd time signatures, or at least not by "later" in their careers...

• The Beatles
• Led Zeppelin
• Black Flag
• Pink Floyd
• Cop Shoot Cop
• Sting
• Nine Inch Nails

"Progressive" rockers, for whom it's just part of the genre

• King Crimson
• Yes
• old Genesis
• Frank Zappa
• Rush
• Marillion
• Dream Theater
• Mr. Bungle

Performers who seem to have stopped using odd time signatures

• PJ Harvey
• Peter Gabriel (at least for So)

Performers who have, like, one novelty song in odd times

• The Cars, Touch and Go (well, ok, and Panorama too)
• The Police, Mother
• Roxy Music, Amazona

Performers who I don't own anything by them with odd time signatures

• David Bowie (he must have some, though)
• The Smiths (They have a "novelty" song, but I don't own it)
• Lisa Germano (although Sycophant does switch back and forth)
• Elastica
• Talking Heads
• Soul Coughing
• Sarah McLachlan

Standout albums for odd-time signatures outside the prog-rock genre:

• Sting Ten Summoner's Tales (two or three songs in 7, and Seven Days in 5--is that a little joke on his part?)
• PJ Harvey's Dry (three songs in 5, and one song in 6 that occasionally drops beats to 5)
• Nine Inch Nails Downward Spiral (not as much, but much more dramatic; one song mixes 7/8 and 4/4, and another alternates between 7/4 and 6/4)

Once I mentioned on talk.bizarre an "Index of Meters", and perhaps I posted an attempt at it, I don't recall any more. The idea would be to attempt to document just what meters do get used. To give you a taste:

• 5/4: You can tap your foot to it. You can even swing it (call it 15/8 if you want). This is, I think, the most popular "odd time" amongst non-prog-rockers, and it seems always to be broken down as 3+3+2+2/8: Paul Desmond's Take Five, the theme from Mission Impossible, Jethro Tull's Living in the Past, Everything's Alright from Jesus Christ Superstar, Seven Days by Sting. DIY by Peter Gabriel is an example of a different breakdown. (Personally, I like the syncopated 3+2+2+3, although I've never heard anyone else use it.)
• 7/8: Most people play this as a 4/4 measure with the last eighth note chopped out--or at least that's the effect it has, creating propulsion and a sense of rushing. It appears several times in Jesus Christ Superstar, and is quite popular amongst prog rockers; Subdivisions by Rush and Any Day Now by Cop Shoot Cop are good examples, the latter one definitely having the "rushing" effect.
• 7/4: However, non-prog-rockers seem to prefer 7/4, since you can tap your foot to it. Often a drummer with play "straight through" it (in 4/4), effectively making it 14/4. (And sometimes a song that is otherwise in 7/8 becomes 7/4 due to the drummer and some misplaced desire to allow people to tap their foot); Pink Floyd's Money is the big one here; Sting's Straight to My Heart is another; and Peter Gabriel's Solsbury Hill reminds me of the "standard" 5/4 pattern. The keyboard break/guitar solo in Rush's Tom Sawyer is also in 7/4, featuring a different kind of 7/4 that I've heard them use in other places.
• 5/8: By all rights, this should be a popular time signature; it's a smaller prime than 7. However, i think it's just too asymmetric for people. 7 is often a "shortened 8", which gives it a propulsive feeling; interpreting 5 as a shortened 6 is very hard, because it's not long enough to get the pattern--i.e. compare 2+2+2+2 -> 2+2+2+1 vs. 3+3 -> 3+2. There are a few dramatic 5s, though. The bit in Jesus Christ Superstar that goes "How can you say that" (and similar bits) sounds to me like 5, although it may not actually be--but in my head it's a string of 5 equally weighted notes, with no subdivision. The Cop Shoot Cop song Nowhere is arguably in 5/8, but since it follows the 3+3+2+2 format, I prefer to think of it as a very fast 5/4. Rush has only one song in 5/8 (whose name escapes me now, it's on Signals), and even there it's only for the verses. The George Harrison song on Sgt. Pepper's is in 5/8, if I recall correctly (it's been ten years since I heard it)--Within You, Without You maybe? Anyway, I think it's just very hard to phrase vocals to fit it, although I personally love the effect, especially with the (extremely common) breakdown of 5/8 as 3+2. Common? Well, 5/8 does get used a lot by certain people in non-vocal situations, and when it does, that breakdown is common. The aforementioned Rush song is 3+2. Non-vocally, there's the intro to Incommunicado by Marillion. Robert Fripp seems very fond of 5, so lots of King Crimson songs have bits of 5/8: the clangorous intro to Neurotica is in 3+2; some of the layered guitar parts at the beginning of Neil and Jack and Me are in 5/8 as well; and the last two songs on Starless and Bible Black have quite a bit of 5/8.
• 9/8: 9 isn't prime, and in fact, 9/8 is usually just a "triplet-time" 3/4, if you know what I mean. It is however possible to play it differently, and I bothered mentioning this since it's part of a song title: Genesis' Apocalypse in 9/8. Also found in Led Zeppelin's The Crunge.
• 11/8: The little transition bit in Here Comes the Sun by The Beatles is 3+3+3+2, although this is made less "odd timey" by the fact that the immediately prior measure drops an 8th note, so you could tap your foot through it (although the rhythm is so strong I doubt anyone would). No others come to mind.
• I can't think of any stand-out 11/4 songs. The Rush song Jacob's Ladder uses alternating 5/4 and 6/4, except the effect is reduced by the fact that chord changes occur in 4/4.
• 13/4: The middle section of Starless by King Crimson is the standout example. I'm not even sure it's reasonable to claim it's subdivided; it simply has a melody which "adds up to thirteen". (The most plausible subdivisions: 8/4 then 5/4, although one might even suggest it's actually 17/8 + 9/8, although since eighth notes are swung this seems inappropriate.) Turn It On Again, by Genesis, is largely in 13/4, but it is more effectively described as alternating 6/4 and 7/4.
• 13/8: Similarly, the middle section to Jacob's Ladder by Rush uses a guitar figure which is alternating 6/8 and 7/8; is that really 13/8 though? The song Surprise, Surprise by Cop Shoot Cop has a middle section which I think is arguably 13/8, because it alternates between the breakdowns 3+3+3+2+2 and 3+3+2+5; given that both appear, I think the intent is for it to be 13, not 6+7 or such.
• Not much point continuing the list, because the trend should be clear now; longer time signatures can usually be broken down into shorter ones, because we naturally want structure. Of course, it could end up just being a sequence of 3's and 2's, but it's more likely that we'll cluster those together. For example, the Rush song Free Will has a structure 6+8+6+7/4; each number is clearly a musical boundary point, so there's little point in calling this "27/4". Similarly, there's a beautiful piano melody in the Dream Theater song Wait for Sleep, whose structure is 5+5+5+4/8 alternating with 6+6+6+4/8. Should we call this 19/8 alternating with 22/8? Or just 41/8?

• Heaven on Their Minds from Jesus Christ Superstar (the bridge)
• Bunches of similar songs from JCS are also in 7/8, although I don't recall their titles: "Roll on up for the price is down", "See my legs I can hardly walk", "What do you think was your big mistake?" "Come with us to see Caiaphas" (or is that the same as the previous one?)
• Rush Xanadu
• Rush Hemispheres (in various places)
• Rush Red Sector A (intro)
• Marillion Lords of the Backstage (half is in 7+6/8, half in 7/8 that's drummed as 7/4 I think)
• Marillion Just for the Record
• Genesis Cinema Show (the extended instrumental section)
• some other old Genesis songs on some albums I've only listened to once
• King Crimson Frame by Frame
• King Crimson Neurotica ("Arrive in neurotica" part)
• King Crimson Model Man (chorus--actually, two other of this album's choruses are in 7, but drummed in 7/4 and 14/4, although the guitar figures generally repeat in 7/8)
• Nine Inch Nails March of the Pigs (7+7+7+8/8)
• Tribe Rescue Me (Ok, you've may never have heard of them, but it's in my collection and I'm being completist. It's actually 7+7+8+8).

There are some great "strung together" bits, like the aforementioned Dream Theater song, and the Genesis song A Fifth of Firth.

On the other hand, it can get silly. With the 80's King Crimson, Fripp started experimenting (e.g. with Discipline and Frame by Frame) with layering one part playing in 7/8 and another in 13/8, thus creating a continually shifting pattern that doesn't repeat for 13*7 8th notes. I hesitate to call that 91/8; unfortunately, the rhythm section often plays 4/4, suggesting that it is best called "an interesting melody in 4/4".

The first song I ever wrote with lyrics was in 13/8. I couldn't really figure out how to make a convincing instrumental in 13/8 where the 13 sounded natural. So I came up with the idea of writing lyrics that wanted to flow in 13/8. I used the metrical scheme /u/u/u// (althought the text is readable with the last syllable short), and then sang each long syllable as a quarter note, each short as an eight; it comes out as 2+1+2+1+2+1+2+2, or 3+3+3+2+2, with no apparent "alternating sixes and sevens". It actually worked pretty well--the song sounded "natural" and flowing. Although the lyrics were kind of lame. I put the chorus in 5/4, and later discovered I had ripped off the chorus melody from Jethro Tull. Oops. And then a friend of mine played me a Rod Stewart song with the same chord changes as my verse--even though I swear I'd never ever heard that song before.