It's a matter of style. Colons still exist and your example, "He has jumped from high places: towers, antenna, buildings and mounts" seems perfectly natural to me.
The colon is more formal, the dash is less formal.
A dash is more emphatic. It is almost like an exclamation point.
The colon is not EXCESSIVELY formal. I suggest you "err on the safe side" and use the colon. The worst that could happen is that people will say "Foreign speakers of English use better English than we do!"
I would expect to see colons in materials like this: factual writing, newspaper stories, encyclopedia articles, textbooks, expository writing, and people who just prefer a more formal style
I might expect to see a dash when the writer is trying to convey a spoken tone of voice.
However, you can't use a colon in front of something that isn't basically a list.
Correct: "I always like ice cream--even if it isn't my favor flavor."
Incorrect: "I always like ice cream: even if it isn't my favorite flavor."
In general, the use of punctuation, all punctuation, is decreasing in modern written English. In part that is because we use shorter sentences, so the comma and the period are good enough--we don't need many of the in-between punctuations marks.