How do I check if a user left the 'input' or 'raw_input' prompt empty?

This also work too

y = input('Number>> ')
while not y:
    y = input('Number>> ')

You know if nothing was entered for the second one because it will raise a SyntaxError. You can catch the error like this:

try:
    y=input('Number>> ')
except SyntaxError:
    y = None

then test

# not just 'if y:' because 0 evaluates to False!
if y is None:

or, preferably, use raw_input:

try:
    y = int(raw_input('Number>> '))
except ValueError:
    print "That wasn't a number!"

For the first one, x will be an empty string if nothing is entered. The call to str is unnecessary -- raw_input already returns a string. Empty strings can be tested for explicitly:

if x == '':

or implicitly:

if x:

because the only False string is an empty string.