How to End a Conversation Without Being Rude

More specifically, what to say:
Wait for a pause and offer a handshake. As the other responds, say, “It was great talking with you” or “I have a few more things to do but I enjoyed our conversation. See you later.”
Offer an apology. “I don’t want to keep you any longer/I can see you’re busy, but it was good to see you.”
Smile and say goodbye. This will communicate you’re friendly. You could add something about being happy you’ve had a chance to talk.
If you want to see the other person again, suggest meeting in the near future. Be specific. “How about next Wednesday morning?” is better than “We’ll have to get together soon.”

Useful, civil phrases to remember:

• I’m afraid I’ve lost track of the time.
• I promised I’d meet [someone]; gotta run.
• I don’t want to keep you.
• This was fun but I’m running late.
• I wish we could talk some more but I'm running late.

I don't like saying something like "I have to leave" because then you have to leave and sometimes you might have a different reason for staying, but still need to end the conversation.

If you are waiting for a gap in the blah-blah-blah, and there doesn't seem to be one, wait for them to take a breath, and then quickly -- but politely -- explain that you have work to do, and that you'll catch them later. Saying you'll talk later is friendly, and most of the time, the person will have time to organize thoughts, so your follow-up conversation is shorter.

If they started the conversation, wait for a break in topics. Pauses in between thoughts are good places to tell the person you have to be somewhere or have to get something done. Note: Pauses in between thoughts does not mean waiting for the person to simply finish a sentence or say "Um..." You really should wait until they finish a thought, out of courtesy.

• Phrases such as, "Can we talk later?" are the best lines to use, because they still maintain a level of interest. But you have to at least ACT like you mean it. Don't be annoyed if the person calls later or tries to start up a conversation again. If you're already ducking the conversation with this person, don't be dragged in a second time! Quickly abort the situation by saying how swamped you are with work or school or home problems. Acting like you dislike your work, whatever the case, and seeming like you'd rather be talking to the person are good attitudes to try in this situation.

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