I have quite a few US and UK promo singles. Most US ones are mono/stereo versions of the same song (with blue and white labels on each side), whilst most of the UK ones are the same as the commercial releases (A and B sides) - there are also some variations with the US Hot Stuff/Fool To Cry.
However, some of the US singles do have "edited" versions, usually with a fade out 30-60 seconds earlier, eg:
It's Only Rock'n'Roll (mono & stereo) 4.46 edit Beast Of Burden (stereo) full 4.24 version b/w 3.20 stereo edit Shattered (stereo) full 3.46 version b/w 2.44 edit Emotional Rescue (stereo) full 5.38 version b/w 4.18 stereo edit (UK version the same) Undercover (stereo) full 4.31 version b/w 3.59 stereo edit (UK version the same) She Was Hot (stereo) full 4.40 version b/w 3.59 stereo edit
Some of these edits have also appeared on compilation albums such as 40 Licks etc.
An interesting one is the US promo of She's So Cold which has the original version on one side and a "Cleaned-Up Version" on the other, which edits out the word "Goddamn" for the sensitive ears of US radio listeners.
I also have a UK promo of Let's Spend The Night Together b/w Start Me Up released to promote the Hal Ashby film (some copies come with promotional material). On the label it says "From the film Let's Spend The Night Together", but are in fact just the Still Life versions...
Then there are the promo 12" singles and 7" EPs...
Two Rare UK Exile Promos aka Demos in the UK. Happy b/w Shine a light and All Down the Line b/w Rocks Off. alternate mono mixes, missing many overdubs==RAW---probably cut before they went to LA to finish Exile..Both tough to get...
Also, Tumbline dice one sided UK demo exists in this same series, but dont have that one...YET!
US ones are easier to find (they had more radio stations than the UK, so I suppose a lot more of them were pressed). They do turn up on e-bay, the more common ones for around $10 usually. UK ones are rarer, I mainly get them from dealers and record fairs, but I have seen some turn up on e-bay (as per Mr Steel's post above).