This one I heard while listening to DFW approach control on a live internet feed (you can listen in too by the links on my 'aviation info page')

These are from atcmonitor.com

The controller working a busy pattern told the 727 on downwind to make a three-sixty--do a complete circle, a move normally used to provide spacing between aircraft.
The pilot of the 727 complained, "Don't you know it costs us two thousand dollars to make even a one-eighty in this airplane?" 
Without missing a beat the controller replied, "Roger, give me four thousand dollars' worth."

A DC-10 had an exceedingly long rollout after landing with his approach speed a little high. 
San Jose Tower: "American 751 heavy, turn right at the end of the runway, if able. If not able, take the
Guadalupe exit off Highway 101 and make a right at the light to return to the airport."

Unknown aircraft: "I'm f...ing bored!" Air Traffic Control: "Last aircraft transmitting, identify yourself immediately!"
Unknown aircraft: "I said I was f...ing bored, not f...ing stupid!"

Tower: "Eastern 702, cleared for takeoff, contact Departure on 124.7."
Eastern 702: "Tower, Eastern 702 switching to Departure. By the way, after we lifted off we saw some kind of dead animal on the far end of the runway."
Tower: "Continental 635, cleared for takeoff, contact Departure on 124.7. Did you copy that report from Eastern?"
Continental 635: "Continental 635, cleared for takeoff, roger; and yes, we copied Eastern and we've already notified our caterers."

The German air controllers at Frankfurt Airport are a short-tempered lot. They not only expect one to know one's gate parking location, but how to get there without any assistance from them. So it was with some amusement that we (a Pan Am 747) listened to the following exchange between Frankfurt ground control and a British Airways 747, call sign "Speedbird 206":
Speedbird 206: "Top of the morning, Frankfurt, Speedbird 206 clear of the active runway."
Ground: "Guten Morgen. You vill taxi to your gate."
The big British Airways 747 pulled onto the main taxiway and slowed to a stop. 
Ground: "Speedbird, do you not know where you are going?"
Speedbird 206: "Stand by a moment, Ground, I'm looking up our gate location now."
Ground (with arrogant impatience): "Speedbird 206, haff you never flown to Frankfurt before?"
Speedbird 206 (coolly): Yes, I have, actually, in 1944. In another type of Boeing, but just to drop something off. I didn't stop."

Billund ATC: Gliders 82 and D5, state position and altitude? 
82: Overhead Coal Lake, 6400 feet. 
D5: Same position, same altitude. 
ATC (cool, dry voice): So should I go get my collision report form ? 

ATC: Say altitude 
Pilot (feeling frisky): altitude 
ATC: Say ALTITUDE 
Pilot: ALTITUDE 
ATC: Say 'Canceling IFR' 
Pilot: Level 8000

Several planes were running up and waiting to take off, many Cessna's including a 337 Skymaster. With all the students and several similar call signs, the controllers were getting a tad confused. The controller finally asked: "Cessna 123YZ, are you the Skymaster?" 
A slightly confused voice with an indeterminate accent replied, after a moment, "Well, my instructor says that I am very good, but I do not think that I would yet be considered the 'Skymaster.'" 

A friend of mine was ferrying his Blanick (a glider) to a nearby airport on the other side of some Class C Airspace. The 182 tow plane had no radio, but the Blanick did. No problem, after departing the glider called, ATC and gave their intentions to cross The Class C airspace. About halfway across, ATC requested a 90 degree right turn. My friend responded. "What do you want me do? Yell out the window?"

A crew in a Baron was taxiing at LAX back in the sixties and encountered one of the (then) new 747's. Both pilot and co- were all eyes as both aircraft approached the same intersection. 
Baron: Uh, ATC, verify you want me to taxi in front of the 747. 
ATC: Yeah, it's OK. He's not hungry. 

Tower: Cessna N1234, be advised wake turbulence - UA 737. [pause] 
Cessna: San Jose tower be advised the Cessna is ahead of the 737. 
[longer pause] 
Tower: UA 737, be advised wake turbulence Cessna 172. 
Someone: Giggles and laughter in background.

Tower controller after several unsuccessful attempts to raise the student pilot whom he has just issued instructions to: "You have to key in the mic...I can't see you when you nod your head." 

I was taxiing out to the active runway in a 172 and I had just dialed up tower and checked the approach which was clear. The weather was 15+ vis and no ceiling. I was just about to call tower for clearance when I heard this. 
ABC: London tower this is alpha bravo charlie on short final 33. 
TWR: Alpha bravo charlie, negative visual contact pull up go around. 
I took a good hard look for the a/c and saw nothing so I called tower and got cleared to go. I heard 2 more renditions of the "On short final" and "Pull up go around" act. On the fourth try the pilot got a bit frustrated about the wave off. It went like this. 
TWR: Negative visual contact pull up and go around. 
ABC: Well look out you window, I'm right bloody in front of you! 
Tower came back very cool and collected. 
TWR: Alpha bravo charlie look down into the centre of the runway pattern. Do you see a big white radar dome? 
ABC: err....negative dome tower. 
TWR: That's because you're not over London. You're over Waterloo-Wellington 50 miles north-east of my position. Waterloo-Wellington tower frequency is 125.00. I think they would like to talk to you. 

ATC: Cessna 1234 What are your intentions? 
Cessna: To get my Commercial Pilots License and Instrument Rating. 
ATC: Cessna 1234 I meant in the next five minutes not years. 

A true story from my Scottish days when a C152 pilot was asked to report his height prior to clearance to enter the zone, replied: "Flight Level Three Thousand, Seven Hundred", upon which the Controller very smartly replied, "Roger, prepare to fire retro-rockets and re-enter the atmosphere!" 
(Flight levels are in hundreds of feet, , so FL 350 means 35,000, so this guy was saying he is at 370,000ft.)

C-150: Tower this is N-1234 can you give us a ground speed please? 
Tower: Roger N-1234 we show you at 110 knots 
Mooney: (Showing off a bit) tower this is N-5678 can you give US a ground speed please? 
Tower: Roger that N-5678 we show you at 201 knots 
F-18: (Showing off a lot and said with a Texas drawl). Heh Heh.. tower how about XXXX, can you give US a ground speed please? 
Tower: Roger XXXX we show you at 580 knots. 
... then in a distant crackly voice, 
"Tower, we'd like a ground speed too please..." 
Tower: Ummmm ahhh .... must be something wrong with our equipment here, I show you at 1500 knots sir. 
"No sir, this is a SR-71. Thank you for the reading." 

Another student, a not too bright woman, was coming in for a landing. The radio in the FBO was set to the ground freq. It seems that she landed on the taxi way. 
The ground controller told her, "please call 555-9876 after you park the plane". 
She answered, "No thank you sir, I'm already married." 

Cessna: Bay Approach, Cessna 12345 over South County Airport at four thousand feet, request permission to land at San Jose. 
Bay Approach: Cessna 12345, Squawk 4567, and do you have Hotel? (the current SJC ATIS) 
Cessna: Negative, we're going to stay with my sister-in-law. 
American 123: Does your sister-in-law have any extra rooms? 

Overheard by a guy giving rides: "Sorry about the rough landing, but I'm practicing for a job at SAS. Next time I'll try to loose your luggage." 

Student pilot to instructor: "Think about it. I navigated through a boiling fluid swirling around a rotating sphere that is hurtling around a fusion reaction source at thousands of miles per hour. This system is moving in a circular motion around a black hole at who knows what speed, while the space it takes up is expanding. And I bounced six inches. SIX MEASLY INCHES! Get off my freakin' back, man!" 

Tower: "Aircraft on final, go around, there's an aircraft on the runway!"
Pilot Trainee: "Roger" (pilot continues approach)
Tower: "Aircraft, I said GO AROUND!!!"!
Pilot Trainee: "Roger" 
The trainee doesn't react, lands the aircraft on the numbers, rolls to a twin standing in the middle of the runway, goes around the twin and continues to the taxiway