Read me first!

All airlines (although see note about TG) appear to give them departing from Bangkok, so the list below is mostly useful for inbound. It's important to remember that this is Thailand so just because an airline has given them out before is no guide they'll be given out in your case. It's worth asking both air-crew and the ground crew at the gate for them, as they're also occasionally forgotten. Thus the list below tends to reflect "this airline has given them out at least once" rather than being any guide to what will actually happen...

List

AI (Air India) - J arrival and departure
AF (Air France) - J arrival (distributed in the jetway leaving the aircraft), J and W departures
AY (Finnair) - J arrival (jetway) and departure
BA (British Airways) - J arrival and departure (BE AWARE there have been instances where cabin crew have not handed out the pass and when asked either only given to the asking passenger or advised they aren't given out)
CX (Cathay Pacific) - J/F arrival and departure, OWE departure
EK (Emirates) - J/F arrival and departure, Gold and above in Y excluded by local rules
EY (Etihad) - arrival (criteria unknown)
HU (Hainan Airlines) - J departure only
HX (Hong Kong Airlines) - J departure and J arrival
JL (Japan Airlines) - J/F arrival and departure
KE (Korean Air) - J arrival and departure, assume F as well
LX (Swiss Airlines) - J departure
LY (El Al) - arrival and departure for J+F plus KD
MH (Malaysian Airlines) - J arrival and departure, OWE departure
NH (ANA) - departure, J also arrival (4/2016)
OS (Austrian) - J departure
OZ (Asiana) - J arrival and departure (no OZ F service in BKK) (no arrival 26/03/16)
PG (Bangkok Airways) - Blue Ribbon (C) or Premier ongoing for arrival and departure
QR (Qatar Airways) - J arrival and departure, OWS (or above) departure
RJ (Royal Jordanian) - J and OWR (or above) departure, J arrival,OWR (or above) in Y (if you manage to find RJ staff at the jet bridge)
SQ (Singapore Airlines) - J arrival and departure or PPS Club/Solitaire, sometimes on request only
SU (Aeroflot) - J arrival and departure
TG (Thai Airways) - F/J have dedicated security area at airport for outbound, for arrivals not given but your boarding pass is sufficient
TK (Turkish Airlines) - J arrival
UL (Sri Lankan Airlines) - J/OWS (or above) arrival and departure
VN (Vietnam Airlines) - J departure only

Notes:

1) Immigration seems to only care about the airline stamp. Recent experience continues to be hassle free when the printed date and/or names do not match or are not filled in. YMMV. Edit: In early June (2015) was told by dragon to fill in the name field on the Fast Track voucher. She then checked to see if it matched BP name.

2) If you're inbound to BKK and have not received a voucher onboard the aircraft, be sure to ask!

3) Fast track vouchers do not have to be used on the date issued. If regular immigration queues are short on your arrival date, it's often worthwhile to pocket the voucher for a different arrival date when you may not have premium access (or to give as a gift to friends/family coming to visit).