Verbs
过 for things you have done before
过 after a verb means you have done it at some point in your life. It is experience, not a finished event.
过 is said with a neutral tone in this job, guo rather than guò, which distinguishes it from the ordinary verb meaning to pass. Unlike 了, it survives the negative: 没去过 keeps the 过, because you are still talking about experience, only the absence of it. The split with 了 lines up with the English difference between went and have been.
Examples
我去过中国wǒ qùguo ZhōngguóI've been to China
你去过吗nǐ qùguo mahave you ever been?
我没去过wǒ méi qùguoI've never been过 stays after 没
我去了北京wǒ qù le BěijīngI went to Beijinga specific trip, so 了 not 过
Watch out
The mistake this causes
Using 了 for a life experience. 我去了中国 reports one trip; 我去过中国 says it is on your list of things done.