What technical reasons exist for not using space characters in file names?

Whitespace characters in filenames can be a right royal pain in the proverbial in many contexts on the command line, and in scripts, where you have to be careful to make sure they are properly escaped so don't look like separators to the commands you are running.

It is just safer not to have them there, even if you are sure the file/dir/what-ever is never going to be used in such a context.

That, and old habits die hard.

In addition to the other answers about command line and old habits, there are also many network protocols which require special care when dealing with filenames containing spaces.

(If you've ever tried to download "Product List.pdf" from a website, and ended up with a file just called "Product", you got bitten by this, because the programmer on the other end didn't know or couldn't figure out the quoting rules for the http Content-Disposition header.)

A lot of the reasons are historical. That doesn't mean that they don't make sense today.

Issues in Portability

When naming a file, you may also have to consider how other (file) systems will treat that file name. A character in a file name may be fine for your system, but it may be an issue for another system.

So, as long as there was the slightest possibility that you may want to be able to access the file easily from an older system, you'd pick only safe character. This may include booting into an old recovery system you kept around or the fear that recent Windows versions are still somehow based on MS-DOS.

Length

A file system may limit the length a file can have. This was even more serious during the days when MS-DOS was limited to 8.3 filenames. So, leaving out spaces enabled you to put more meaningful characters into the name.

Several other file systems also defined strict limits on their file name length. Wikipedia has a table in the article about file system comparison for those that want the details.

Reserved Characters

MS-DOS also defined the space character as a reserved character. This is due to the fact that the space character was used for padding in the FAT. Additionally, MS-DOS did not provide for an escaping system in the shell.

Command-Line Interpretation

Most command-lines I am aware of use the space character as a parameter delimiter. When neglecting to properly escape a filename, it can have dire consequences as parts of the filename can be interpreted as parameters to the application you wanted to call.

Consider the difference between

rm foo bar

and

rm "foo bar"

The WikiPedia article linked above even points out ambiguity introduced by missing to properly escape a command:

Ambiguity can be prevented either by prohibiting embedded spaces in file- and directory names in the first place (for example, by substituting them with underscores '_'), or, if supported by the command-line interpreter and the programs taking these parameters as arguments, by enclosing a name with embedded spaces between quote characters or using a escape character before the space, usually a backslash ('\'). For example

Long path/Long program name Parameter one Parameter two ...

is ambiguous (is "program name" part of the program name, or two parameters?); however

Long_path/Long_program_name Parameter_one Parameter_two ...,
LongPath/LongProgramName ParameterOne ParameterTwo ...,
"Long path/Long program name" "Parameter one" "Parameter two" ...

and Long\ path/Long\ program\ name Parameter\ one Parameter\ two ...

are not ambiguous.

Uniform Resource Locators (URL)

When trying to describe the location of a file, using a URL, spaces need to be escaped.

Characters can be unsafe for a number of reasons. The space character is unsafe because significant spaces may disappear and insignificant spaces may be introduced when URLs are transcribed or typeset or subjected to the treatment of word-processing programs.

Source: RFC1738

Thus, a space has to be replaced with a %20 instead. This makes the filename part of the URL less readable and, thus, makes people avoid it in the first place.

Spaces are encoded or converted to %20 in file names on the web, which may make it harder to manage a site's assets.

Having Image 1.png and Image%201.png is confusing. It's easier to use Image001.png instead.

This really falls under the same category as escape sequences for command line.