Looking through the Bulbapedia learnset entries for each HM move, I have found no instances within each HM set where a Pokemon learn it, but its evolution can not;
- Cut (HM01)
- Fly (HM02)*
- Surf (HM03)*
- Strength (HM04)
- Flash (HM05 Gen 1-3)
- Venonat/Venomoth can to learn Flash in Yellow, but not in R/B. Venonat loses the ability to learn flash in Gen 2
- Hoothoot/Noctowl lose the ability to learn Flash in Gen 4, although it's no longer an HM.
- Defog (HM05 D/P/Pt)
- Whirlpool (HM05 Hg/Ss - HM06 Gen 2)
- Waterfall (HM05 Gen 5 - HM07 Gen 2-4)
- Rock Smash (HM06 Gen 3-4)
- Dive (HM06 Gen 5 - HM08 Gen 3)
- Rock Climb (HM08 Gen 4)
There are a few fringe cases that pop up in earlier generations (Mostly between Red Blue and Yellow) where a Pokemon might learn the HM in one game and then be traded to another where its evolution cannot. There may also be unmentioned cases of this between Gens 1 and 2, however the Time Capsule was fairly restrictive in what could be sent back.
*Pikachu is an interesting side case - As there are event and side-game transfers that can give you a Pikachu with Fly, or even Surf (there's also a surfing Pichu). However in none of these instances can Pikachu be taught the moves from an HM.
Beyond Gold, Silver, Crystal, and the modern remakes, HeartGold and SoulSilver, none of the flagship pokemon games have ever spanned more than one region (though several have included isolated islands or otherwise remote areas). So "as far as we know", only the Johto and Kanto regions are confirmed to be nearby (and are, in fact, adjacent).
As mentioned in Bulbapedia, however, the first four generations are all analogous to real-life parts of Japan, while the fifth generation maps to the New York Metropolitan area, and Kalos (6th and current gen) maps to real-world France.
I wouldn't go so far as to say that the previous regions are completely ignored (Oak, at least, has made it to Hoenn on more than one occasion), but beyond the previously mentioned exceptions (and monsterous residents, which feature previous generation pokemon in their "National Dex"), each region is pretty much distinct.
Best Answer
There are some old pokemon that learn new attacks, notably due to the introduction of new attacks (new mechanics like day/night, weather or through an entirely new type: Steel or Fairy). But it's also possible that some already existed attacks were added to the move-set of an already existed Pokemon.
Here is a little example: