While I wouldn't say it's THAT significant, there is one other advantage to fixed-width fonts that I've experienced. Due to the fact that they align vertically, sometimes they expose mistakes if you're constructing data in a table-like fashion. Or when you have a bunch of copy/pasted lines that differ only in the parameter values. Like, "Hey wait a minute... this line is 1 char wider than the previous one. Oh, whoops, I fat-fingered something there".

I wish I had more specific examples and could quantify it better, but I know I've caught quite a few errors this way.

This exactly. Most recently I had a script that was calling functions with fixed width data sets (IDs, credit card numbers, birthdates, etc..), and typos were significantly easier to find due to the data and fonts both being fixed width.

This is because we don’t have any decent rich formatting options available for code in a plain text file. You could totally find those errors in an excel spreadsheet, and excel doesn’t default to using fixed-width typewriter fonts.

Maybe it's because I've only used fixed-width fonts for programming and have gotten used to it - but I find fixed-width fonts significantly easier on the eyes.

But would you ever read a novel using fixed width fonts? Modern typography uses variable width fonts for good reasons.

I find type writer fonts to look horrible since I’ve gotten used to variable width fonts. It’s like immediate eye strain for me. But you have to choose a good font, times new Roman won’t work.

I used DejaVu Mono Book for quite a while, I had no problems with it.

Only when coding or always, for example books and websites including this one?

Only when coding or working with raw text, I use variable-width fonts everywhere else (reading, browsing the web, etc).

And aligning text in some indentation styles