I deal with this on a daily basis. First of never take it personally, it is the company they are mad at (or their spouse, or the world or themselves), not you.

Second never lose your temper or your cool, kill them with kindness by remaining cool and polite no matter what. Some people do this kind of behavior to get a rise out of you, never let it happen. Sometimes they just need to vent. If you let them go for a bit they run out of steam (not always but some) and it you remain calm and cool, some will calm down and realize they are being an ***.

If you need to vent do it, later when you are not on the phone.

Thirdly if they get too abusive ( in my company at least) let them know and hang up if they can't behave reasonably.

I know it may be different in different kinds of businesses though.

We also have notes on some accounts to warn others if someone is always rude or has other issues.

Laugh it off, some people are just jerks.

In some cases asking them what they would like you to do. If it is an unreasonable request, off them a more reasonable solution to see if something can be done. Though sometimes there may not be a solution if you did everything right and they are just a special snowflake who thinks that rules and policies only apply to others, or that you have the ability to alter the time space continuum and change the laws of physics.