Hmm this for me depends on a lot of things. If I've been in a relationship for x amount of years and I reject him then he needs to work his arse off and come back because I may give him another chance. If it's a first date then take it gracefully and move on. I've had so many guys become abusive because they didn't handle rejection well. If it's a few months then you can try coming around again depending on how much she was into you, but it's likely it won't work. As for being friends it will never work as long as one of the two has feelings for the other. If there's no longer any feelings and you're 150% certain then go for it. But can you handle another guy being all over her in front of you?
Usually the guy is rejected for a reason. For example maybe because she likes someone else, she isn't physically attracted to you etc. Unless she specifically says "maybe in the future... just not right now" or "i don't wanna lose our friendship" then just stay friends. Unless she specifically says so, just GTFO.