How do I do a case-insensitive string comparison?

Assuming ASCII strings:

string1 = 'Hello'
string2 = 'hello'

if string1.lower() == string2.lower():
    print("The strings are the same (case insensitive)")
else:
    print("The strings are NOT the same (case insensitive)")

As of Python 3.3, casefold() is a better alternative:

string1 = 'Hello'
string2 = 'hello'

if string1.casefold() == string2.casefold():
    print("The strings are the same (case insensitive)")
else:
    print("The strings are NOT the same (case insensitive)")

If you want a more comprehensive solution that handles more complex unicode comparisons, see other answers.