You can use map with the unbound method str.split:
>>> map(str.split, open('testFile.txt'))
[['Hello', 'World'], ['How', 'are', 'you?'], ['Bye', 'World']]
In Python 3.x, you have to use list(map(str.split, ...))
to get a list because map in Python 3.x return an iterator instead of a list.