OK, back to the actual question, below is an anecdotal list, out of date for sure.
Anyone got any updates (aside from deleting the carriers no longer with us?) I suspect that the majority being in the approved list is no longer the case post 911.
--------snip from the web-------
Airlines who (allegedly) approve(d) of GPS Use:
Air Canada . .Air New Zealand . .Air Malaysia . .Ansett Australia (No official policy, but do not prohibit use.) . .Britannia Airlines . .British Airways . .Canadian Airlines . .Cathay Pacific . .CAAC (China Airlines) . .Continental Airlines (as of November 2000) . .CrossAir . .Delta Airlines . .Egypt Air . .Icelandair . .Jet Airways (India) . .LOT Polish Airlines . .Maersk Air (Denmark) . .Qantas . .Reno Airlines . .Singapore Air Lines . .South African Airways . .Southwest Airlines . .Sun Country (Regional USA) . .Swissair . .United Air Lines (may ask if your GPS is FCC Class B approved. All handhelds are. Show them in the manual.). .US Airways (was US Air) . .Vanguard Airlines . .Virgin Airlines
. .Airlines which OFFICIALLY DO NOT APPROVE the use of GPS receivers at ANY time during flight.
(*) Individual Pilots may allow GPS use.
Alaska Airlines (as of 04/01). .Air Tran . .America West Airlines . .American Airlines (as of 21 July 2000) . .EasyJet (UK) . .FinnAir . .Hawaiian Airlines(*) . .Horizon Airlines(*) . .KLM . .MidWest Express . .Midway Express . .Northwest (as of 2 Sept 2000) . .Ryanair (Irish) . .SAS (Scandinavian Airline System) . .Spirit Airlines . .TWA . .Varig Airlines