How do you break off a conversation or meeting with a 'clinger' type person?

You probably know the drill.

They talk incessantly. They won’t get off the telephone, or if in person, you cannot walk away from them or break off a meeting or make them leave if they are in your home, They pretend not to get or fail to acknowledge normal cues that you have to leave.

Sometimes it seems you just have to hang up on them or walk away, upsetting them. Such people cause me to lose sleep or time or get off my normal schedule.

It may be rude of me, or of them, but I resent too much incursions into my personal time and space. And often times I really DO have somewhere else more important to be.

How do you end a conversation, meeting, or telephone conversation with someone who believes they’re pouring out their heart to you, and you’re just walking away—when in reality I need to be somewhere else or be sleeping?