I used to work in a call centre for life insurance and endowment policies so while there were not any specific customers I could complain about, there were 4 types which used to annoy me the most.
1) Data Protection Breechers. These were people ring on behalf of someone else wanting information. Unfortunately, UK data protection laws meant I could only give the information to the policy holder or a named person (these are the same rules which means companies can only speak to the bill payer when you ring, we don't do it on purpose to wind you up). Of course, everyone who rings wants you to make a special exception just this once and just for them. The highlight for this was one person who, even after I told them I could face jail time and/or a fine for giving them information, refused to hang up for half an hour. Linked with this are the people who won't/can't read between the lines. Even though I couldn't give out specific information, there was a surprising amount you could give if they asked the right questions or I was in the mood to be helpful and give leading answers. For example, someone was paying an endowment for their Grand-kid ad wanted to know when it matured and payment made. Because they arn't the policy holder (kid owns it once they hit 16), as the payer I could tell them when payments would stop and so essentially answer the question. Even with obvious things like that, there were those who still couldn't figure it out.
2) You'll be hearing from my Lawyer! These were always the most entertaining. I got threatened with multiple lawsuits because I was accused of losing documents, with-holding money, giving out information to the wrong person etc, but they never go through with it mainly because they realise they would lose. Small tip: If you send claim forms, official documents etc to a company, they arn't leaglly accountable until that document has arrived in the building. If the post office lost it, you're complaints with them, not us.
3) I want to speak to your manager. These were always the worst. These are people who don't like what you've told them and so demand to speak to your manager even though the manager can't do anything either. The amount of time some people waste because they refuse to believe what people tell them and so keep trying to go higher is funny. Small tip 2: If you ever ring a call centre where there's been even the slightest bit of trouble before (or not, your choice), automatically ask to speak to a manager. They can (or at least should be able to) do anything the person who picked up the phone can do plus extras if your case is complicated and so will end up saving you time. Just please believe them when they say theres nothing they can do at this time.
4) The "One Minute To"'ers. These are the people who, after getting the call centre number with the call centre opening times displayed clearly next to it, decide to call 1 minute before the lines closed. When I was on the late shift, we used to take it in turns to stay ready to take a call while everyone else took themselves out of the phone line. The record for staying late (to my knowledge) was over an hour after the shift ended. This is why I ring call centres around quarter past the hour.
*looks up* wow, do I sound bitchy.