I made a verbal agreement with representative of a broadband connection, but when I got my bill it wasn't the agreed connection plan I was applying. Can I sue the company for this error. I couldn't contact the representative with whom I made the agreement and he left the company because of the dispute/problem.

You can sue anyone for anything if you're in the USA, but lots of luck collecting money if you have nothing in writing (have no idea about other countries). Think about it: all the company has to say is they have no record of the conversation. So it's your word against theirs.