A Regex that will never be matched by anything

Leverage negative lookahead:

>>> import re
>>> x=r'(?!x)x'
>>> r=re.compile(x)
>>> r.match('')
>>> r.match('x')
>>> r.match('y')

this RE is a contradiction in terms and therefore will never match anything.

NOTE:
In Python, re.match() implicitly adds a beginning-of-string anchor (\A) to the start of the regular expression. This anchor is important for performance: without it, the entire string will be scanned. Those not using Python will want to add the anchor explicitly:

\A(?!x)x

This is actually quite simple, although it depends on the implementation / flags*:

$a

Will match a character a after the end of the string. Good luck.

WARNING:
This expression is expensive -- it will scan the entire line, find the end-of-line anchor, and only then not find the a and return a negative match. (See comment below for more detail.)

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^* Originally I did not give much thought on multiline-mode regexp, where $ also matches the end of a line. In fact, it would match the empty string right before the newline, so an ordinary character like a can never appear after $.