Inspired by this thread, I was reminiscing about a flight from Heathrow to Newark. Shortly into the flight, the Captain came on the speaker, and said:
It took a couple of seconds, but the whole plane burst out laughing. And the Captain never completed his thought.
Heard any classics? I hear SouthWest is great for that sorta thing.
One Southwest stewardess on one of my flights to LA apparently wanted to be a comedian. The only line I remember is, “Pushing the button with a picture of the light bulb will turn the light bulb on, but pushing the button with the picture of the flight attendant will not turn the flight attendant on.” Needless to say, about half of the plane immediately pushed their call buttons.
Southwest is indeed great for this stuff. On a flight to Phoenix last year, we were told during the safety briefing:
“If the cabin should suddenly depressurize, an air bag will drop from the ceiling in front of you. At that point, stop screaming and put it on. If you are traveling with a child, or someone who acts like one, put their mask on first…”
My uncle was on another Southwest flight where he says they actually let a passenger be a stewardess, because she wanted to be one eventually. So the girl went around helping people and passing out drinks and such. At the end of the flight, he claims the following announcement was made:
“We’ll be making our approach into Kansas City in just a few minutes. We’d like to thank Gena for doing such a wonderful job as a student-stewardess. She’s done so well in fact, and is so enthusiastic and competant, that we’re going to let her land the plane!”
Both of the previously mentioned comments were made on a flight I had on SouthWest (only used them once, round trip). I wouldn’t be surprised if they have a script they use on all their flights.
Heard when approaching Copenhagen:
“We’re approaching Copenhagen Airport and will begin descent in a few minutes. <seatbelts, upright position, yaddayadda> Oh, and the captain informs me that for your safety and convenience, he has decided to deploy the landing gear. Thank you for flying SAS.”
A FOAF claims to have heard this while waiting for the plane to leave the gate: “We’re sorry about the delay, but the machine that tears the handles of suitcases has broken down and it’s being done manually.”
S. Norman
Small nitpick: they probably told the passengers to put theirs on first, then help the kids.
On a British Airways flight from London Heathrow to Amsterdam, the captain came on the intercom as we taxied to the runway.
“Ladies and gentleman, we will soon be taking off from runway 4. As is standard operating procedure, we will dim the cabin lights during take-off. Enjoy it while it lasts, because it’s probably the only chance you’ll get all week to be alone in the dark with a BA flight attendant.” 
This is not exactly on topic, but I thought it was great. I was waiting for a flight at a tiny regional airport in Arkansas. Our plane came it, but then it got taken away and they announced that it was delayed due to mechanical problems. There was another flight about to leave for the same destination. A stressed out businessman starts yelling and swearing at the woman on the gate trying to get on the other flight. She calmly tells him that he has to go back to the ticket counter to change his ticket. As soon as he runs off, she goes to the gate, waves to the pilot, and he backs out and takes off. She then says just loud enough for those of us nearby to hear, “Nobody swears at ME and gets on an airplane!”
“For those of you who can swim, land is to the left. For those of you who cannot swim, thank you for flying Aeroflot.” [sub](Okay, okay, so it’s not a real announcement, but it should be!)[/sub]
This wasn’t an announcement, but a parting comment from a flight attendant as passengers were deboarding. This was a flight with a large and rather obnoxious group of a couple dozen college-aged travellers sitting in the front of the coach section. For some reason we made an ungodly hard landing. The tires hit the runway so hard that one of those little oxygen-mask doors popped open. The masks fell down and bonked two of the obnoxious group on the heads. A cheer was heard from the rows behind.
As we were leaving the plane, one of the attendants was apologizing for the landing. “But at least now,” she smiled, “you know there really is something behind those little doors!”
I had originally heard this as Lufthansa, but whaddya gonna do. 
My father’s a 30-year veteran of SAS. I’ll give him a call and see what stories he’s got to tell.
From a Southwest Airlines flight attendant: “Welcome aboard Southwest Airlines. To operate your seat belt, insert the metal tab into the buckle, and pull tight. It works like every other seat belt. If you can’t figure it out, you shouldn’t be in public unsupervised. In the event of loss of cabin pressure, a thing that looks like a margarine tub will drop out of the ceiling. Please refrain from screaming, put the margarine tub over your own face first. If you’re traveling with a child place it over the child’s face next, and if you’re travelling with more than one child, decide now which one you love more.”
And from a Southwest Airlines pilot: " The weather at our destination is 50 degrees with broken clouds. We’ll try to get them fixed before we land."
It’s not really a cabin announcement, but still…
Conversation heard on ATC Frequency
Unknown pilot: I’m fing bored!!
ATC: Whoever just transmitted last please identify yourself right now!!
Unknown pilot: I said I was fing bored not f***ing stupid
On a flight to San Francisco from New York, before (delayed) takeoff: “Sorry takeoff has been delayed, but we can’t get the flaps on the wings to work. We’re calling someone who knows how to fix them.” Thirty minutes later: "OK, we THINK [!] we’ve got those flaps working now, so we’ll be taxiing for takeoff . . . " There were a LOT of drinks served on that flight . . .
While flying over some mountain range or other: "We are now cruising at 30,000 feet . . . I mean, 25,000 feet . . . No, 29,000 feet . . . "
On a SouthWest flight from OKC shortly after takeoff
If you look to the right you can see my apartment.
On a flight delayed out of St. Louis (I don’t remember the carrier) we had been sitting at the gate for a while when it was announced that the plane had some mechanical dificulties. Right after the announcement beneath me someone started hammering on something to knock it back into place. Everybody heard it but I could feel the pounding right under my feet. I was so tempted to get off.
Tavalla – not apocryphal at all. It must be a script, because I’ve heard the exact same thing (minus the “margarine tub” description, though).
SouthWest has a reputation as a little more laidback airline, and I’ve heard many jokes from pilots and stewardesses. Sounds like they’re probably given a list of them and told to pick and choose, because some of the others on this page sound familiar as well.
This thread has gone long enough without a good link.
Used to be the only flights you could get out of our local airport were very small prop planes, with maybe a dozen passenger seats. You know, the ones where the pilot estimates everyone’s weight by eye and tells you who should sit where keep the plane balanced?
One time, the copilot turned around (there being no door between the cabin and the cockpit, of course) and eyed the three passengers on the flight. “You guys heard the safety briefing?” All three of us responded in the affirmative. “Good,” he said. “I’m skipping it and we’re taking off. Don’t tell the FAA.”
Also heard on a Southwest flight:
“In the extremely unlikely event of a water landing between Nashville and Raleigh-Durham, your seat cushion may be used as a floatation device. After dog paddling to safety, feel free to keep your seat cushion as a gift from Southwest, our way of saying thanks and no hard feelings.”
Also heard on Southwest:
“There may be fifty ways to leave your lover, but there’s only six ways to get off this plane if it crashes.”
Robin
From a flight attendant on an American flight from New York to Buffalo, attempting to make the standard preflight safety announcement …
FA: Ladies and gentlemen, if you will give me your attention …
People: (not paying attention)
FA: Ladies and gentlemen, your attention please …
People: (not paying attention)
FA: Ladies and gentlemen, welcome aboard flight 645 to CINCINNATI
People: !!!
FA: Thank you for your attention. Now, I would like to say a few words about the safety features on today’s flight to Buffalo …
While on a Delta flight with my mom, our pilot came on and said “Good evening, my name is Captain Robert Jones, but you can call me Captain Bob.” The rest of his flight announcements sounded as if they were made by a children’s show host "This is Captain Bob, and people on the left side of the plane might be able to see Niagara Falls … This is Captain Bob, and it seems we’re heading into a little rough weather … " I could tell that my mom, who is rather formal, was contemplating her dismay at meeting air disaster in the hands of someone calling himself “Captain Bob.”
More fun from SWA:
“Ladies and gentlemen, we have a special guest on board with us today. He is eighty-five years old and this is his first time on an airplane!! So let’s give a nice round of applause for our pilot, John!”