For completeness, you can also use:
mystring = mystring.strip() # the while loop will leave a trailing space,
# so the trailing whitespace must be dealt with
# before or after the while loop
while ' ' in mystring:
mystring = mystring.replace(' ', ' ')
which will work quickly on strings with relatively few spaces (faster than re in these situations).
In any scenario, Alex Martelli's split/join solution performs at least as quickly (usually significantly more so).
In your example, using the default values of timeit.Timer.repeat(), I get the following times:
str.replace: [1.4317800167340238, 1.4174888149192384, 1.4163512401715934]
re.sub: [3.741931446594549, 3.8389395858970374, 3.973777672860706]
split/join: [0.6530919432498195, 0.6252146571700905, 0.6346594329726258]
EDIT:
Just came across this post which provides a rather long comparison of the speeds of these methods.