Moving MP3 files from one directory to another using regex
Constants like '/home/rich/Downloads/' could be made into variables, for example:

src_dir = '/home/rich/Downloads/'
dest_dir = '/home/rich/Music/Songs/'


This would make it clear what they mean, and would avoid duplication if you need to use a constant more than once.
There are three problem in the regular expression.

First, the parentheses are unnecessary — they capture whatever they match for future use, but there's no future use here.

Second, the dot has a special meaning in regular expressions — it matches any character. If you want to match a literal dot, then you need to escape it.

Third, the regular expression is not anchored and that means it can match anywhere in the string. For example, it will match the filename "not.actually.an.mp3.wav".

The regular expression should be r"\.mp3$".
There's no need for a regular expression at all, you could just call os.path.splitext to get the extension:

for f in files:
    _, ext = os.path.splitext(f)
    if ext == '.mp3':
        shutil.move(f, dest_dir)

In fact there's no need to do that, because you could use glob.glob instead:

for f in glob.glob(os.path.join(src_dir, '*.mp3')):
    shutil.move(f, dest_dir)

It seems like overkill to use Python for this, because it would be a one-liner in shell:

mv ~/Downloads/*.mp3 ~/Music/Songs/