I never use them to replace a comma, certainly, and only rarely a colon.

I find parenthesis often awkward or too heavy, so may use the m-dash to replace those. Especially if what might have been a parenthetical is going to terminate a sentence, an m-dash is much cleaner, as it doesn't need a closing mark, and a terminating paren right before a period looks awful. For long potential-parentheticals that do terminate before the end of the sentence, the m-dash takes up more visual space and marks the beginning and end more-visibly, making for easier scanning. One ought probably re-write to avoid parenthetical statements most of the time in the first place, when there's time, but sometimes they're desirable for stylistic reasons, or just because one lacks the time to improve a draft.

I also use it as a "classier" version of the ellipsis. It doesn't replace every use, but it replaces very-casual, colloquial use of that mark as a kind of harder-comma. Looks much better, I think, and serves the same purpose.

As for the semicolon, I'd never shy away from the semicolon when I can get away with it, but use them rarely nonetheless. I don't think I ever replace them with the m-dash, though. As inline list separators they're great and an m-dash would be an awful replacement, while as soft-periods, they're fine, though most of the time I just use a full period—but not an m-dash, not if a semicolon could have worked.

I do think they're more at-home in, say, fiction than technical writing, but I like having them in my toolbox in any case.