Spaces are not the end of the world, but very annoying:
On a bash command line, they make it harder to handle a list of files returned by a command as argument to another.
On the command line (lin or win), they require escaping or quoting when used as arguments or script/executable names.
On many programs, if you cut&paste the complete path to the file (for example in a network drive), you can click on the path and it will access the file, but spaces in filenames or directories breaks that (and it's not bad programming, the program simply can't guess where the link ends).
When you mention the name of the file in a documentation or message, it may lead to misintepretation, and it's just fugly:
"You can find more information in the attached document file.pdf".
What is the name of the file? it can be "the attached document file.pdf", "attached document file.pdf", "document file.pdf" or "file.pdf".
Also when mentioned in a text, the file name may end up split in separated lines or even pages, and will more likely be subject to autocorrect.
When copying the file name in a text, in most environments you can double-click to select the whole name, but it doesn't work if it has spaces.
Now, if you never ever type or copy/paste a file name, and only ever access files through a graphical interface, then it makes no difference.
But then you start getting to comfy and if anything goes, why not non-ascii chars too? And that opens a different can of troubles.
Also, hasn't been said yet, but when a file name with a space is uploaded to the net, the url will replace spaces with "%20" (for technical reasons), making the URL looking bad
(but still not mandatory to replace spaces by underscodes)
Example: http://example.com/the%20file%2042.png vs http://example.com/the_file_42.png
It hasn't been necessary in a long time, unless you're a developer who frequently needs to type in filenames in everywhere (since the command line needs extra protection against spaces and other symbols)
The OS (Windows, Mac, Android, etc) handles thar all for you so you don't have to worry about it (unless you happen to use a badly-written program that doesn't understand spaces, but this is super rare to begin with, and more protected against as time goes on)
Even non-developers may hate spaces in filenames, when links to the file you send in a message don't work because clicking on them uses only up to before the first space.
I maintain a number of Drupal websites as part of my job. Our stakeholders have varying degrees of familiarity with the ins and outs of computing.
A few months ago I got a ticket from one of our stakeholders. Apparently PDF files were broken across large swathes of their site. What happened was Red Hat pushed through an update to apache that closed some security loopholes. As an unexpected side effect, it also meant that any files being served from Drupal's private file system would break if the files contained spaces in the names. No rewrite rules seemed to fix the issue; we ended up having to go into the rendered HTML and replace all the spaces in the links with '+' signs. They are now told to make sure future files have underscores instead of spaces in the filename.
So yes, in some cases you still need to use _ (or some sort of non-space character) in file names, even today.
That depends, if you have the fortune (misfortune?) of using the CAD software Creo/ ProE from PTC then spaces are verboten since they haven't progressed from the days where the software was written for UNIX.
Just in general? No. But I may still use spaces or camel case sometimes on Linux because it makes it a little faster for me to reference a file without escaping the spaces
Personally, I try to keep some rules for myself while using a system. I used to use spaces for readability, but then it was kind of hard to remember all the names of my files, so i just went with a conceptual naming. I now use keywords and some classification like numbers or date before the keywords, it has helped me to find files quicker and with less words than before.
I'd still advise against it if you're using Windows. A space is interpretered as more than a single character meaning you'll hit the 255 character limit for paths quicker if you have a large folder structure. I've seen this happen many times in my time as a support technician.