randrange is the fixed randint, which works just as you'd expect. It's far preferable to randint, for the aforementioned reason, and ever since I started using it all those annoying off by one errors that randint kept giving me vanished.

The one thing I still use randint for is rolling dice. randint(1,6) is the equivalent of a six-sided die, and is that bit more readable as such than the equivalent using randrange.

But for any other purpose, randrange beats randint hands down. Off-by-one errors, be gone!