Which MacBook Pro forbidden to travel by plane?

Like many said, it depends on the airline. At least in the United States, the FAA says that it has to be a device subject to a specific battery recall. You're supposed to be able to enter the serial number here and get an answer as to whether it's been recalled. I understand that if an MBP has received the battery replacement under the recall, it will note that it's not on the recall list.

15-inch MacBook Pro Battery Recall Program - Apple Support

Those Australian airlines were mentioned. Qantas says that all 15" MacBook Pros of any vintage must be in carry on and turned off. Virgin Australia says that all "MacBook" computers can only be transported as carry on. I'm thinking it can't mean my late-2008 polycarbonate MacBook with the battery removed, but by the letter of the law I suppose it would be banned in check in baggage.

I'm sorry if I'm not more specific, but it's hard to give a definitive answer because different national civil aviation agencies are applying their own requirements, and each airline may also have its own requirements.

That model is not recalled. The article below describes the recall. Enter your serial number into the field provided, and when it says yours in not part of the program, PRINT the article (with YOUR serial number showing) and place it with your computer. The serial number is also silk-screened on the bottom of the computer for quick reference.

15-inch MacBook Pro Battery Recall Program - Apple Support

This in NOT any kind of official policy, this is just common sense.

That may not be enough when dealing with airline security.

Australian Arlines are, at the writing, refusing to allow aluminum MacBooks in checked luggage, so carry-on is your only option there..

I had mine replaced. The Product Repair Summary paper I got back with the product shows the serial number, and that the battery was replaced. For my situation, that is the document to have.

Just for interest, in just over a week after the repair was completed, the online status for my serial number has been updated to:

 The serial number you entered is not eligible under this program because either:

• It's not in the affected serial number range.

• Our records show that your device has already been serviced as part of this Program.

You have to think about it for a minute, but is now says my computer is not a danger.

what MacBook Pro do you have?

by year, early mid late, screen size and processor speed?

Call the airline and ask them.