Ha ha. You can use it anytime to replace the word 'NO' in an answer. But be aware that's informal so you shouldn't use it in formal setting like a job interview or business meeting :)

Use nope to mean no amongst friends, otherwise you'll be regarded as an uneducated person.

I ever used "nope" with an internet friend who is non-native speaker when I wana say "no" but he though my name is "nope" :) so sometimes it can be misunderstand among you and other.

Your Question should have been "when can i use the word of nope?" Not "i can"....:)