Hmm, probably a tie between:
1. A customer calling in when I was doing customer service for Cingular Wireless prepaid phones. He stated he was overcharged for a text that he didn't send. I checked his usage history for the time in question, and so nothing out of the ordinary. There were no duplicated time stamps, no unusual numbers, the numbers listed at that time were numbers he called all the time. So I told him that I couldn't refund the charge of 10cents ($0.10) because the system showed regular usage. He got mad and insisted that I give him his 10 cents, I again refused. He then proceeded to say the following:
"Gimme my money dawg!"
"I'm sorry sir I can't give you that refund, the charges are valid."
"GIMME MY MOTHA FUCKIN MONEY DAWG!!"
"Sir, please stop yelling at me, I'm sorry but I can't..."
"FUCK YOU!! GIMME MY MONEY!! I LIVE IN THE UNITED STATES OF MONEY DAWG!! GIMME MY MONEY!!"
".....*slowly process that someone actually said United States of Money un-ironically* "I'm sorry sir, but I can't give you that refund, the charges are valid, if you continue to cuss me out, I will terminate the call"
"FUCK YOU!!"
*click*
Example 2:
I was working at Books a Million, at the register, and I had a long line of people. No big deal, they were all relatively polite, and the line was moving along, but I had to ask each of them if they wanted a Books a Million member card. I had to ask, it was required as part of my job. But hey, no biggy, I'm a good enough salesman that my sales pitch was convincing to the people behind the person I was working on, and I got like 3 new card sales in a row. Then guy number 4 comes up, with a check, to buy a newspaper. He interrupts me mid-pitch, and is like "No, I don't want it, I don't want it." I pause for a second, as he threw off my mental routine, and then went into the next thing I was required to ask about. "Would you be interested in...." *he slams his palm down on the counter over and over, loudly. "NO!! JUST SELL ME MY DAMN PAPER!" I check my impulse to smack him on the head with the nearby heavy object, and just ring him up and get him out of the shop. About 2 seconds later, my supervisor comes up, asking me if I'm ok, because I clearly looked ready to beat someone up. Which is significant, because I generally don't get flustered by assholes. I've done customer service long enough that it rolls off me like water off a duck, but this guy, for whatever reason just hit my buttons.
Those are the two rudest customers I can think of offhand.