Some but not all carriers allow passengers to use their CPAP machines
in-flight.

Some of these carriers have been known to allow passengers to use CPAP in the past:
United Airlines
Qantas
Swiss Air
Argentine Airlines.

But before traveling, passengers should contact their airline to check whether any requirements or restrictions apply.

QANTAS offer a PDF file online for web users;

http://www.qantas.com.au/infodetail/flying/beforeYouTravel/mediform.pdf

Some requirements set out in this form are:
Get a letter from a doctor stating the need to use nasal CPAP or bilevel equipment
Obtain approval from Qantas Medical Services for use on the flight
Have a copy of the approval letter from Qantas
Arrange seating close to a power point on the aircraft

Some airline website addresses are:

QANTAS – www.qantas.com.au

VIRGIN BLUE – www.virginblue.com.au

UNITED AIRLINES – www.united.com