In my opinion, the best game like Airtaxi is
Spacetaxi 3. Up to 4 players can play simultaneously in team or competitive modes and it has just tons of really fun levels.
There's also the excellent
Ugh!. Up to 2 players can play simultaneously and it has beautiful graphics. One of my all-time favorites.
The Executioner has great graphics but is also extremely hard.
Then there's
Zarathrusta which is also pretty good but again quite hard.
The PD Game
Fleuch 2 is also a lot of fun. It is very similar to the original Thrust on the C64.
Concerning multiplayer competitive games,
Mayhem and Bratwurst come to my mind, but there are a lot more (see previous posts).
On other systems:
Exclusively on Atari ST, there's the excellent
Oids. Sadly the scrolling is jerky. What a bummer
.
On NES, there's the great
Solar Jetman: Hunt for the Golden Warship.
On Genesis, there's
Sub-terrania, which looks good. I don't really like to play it all that much. It feels weird to me.
On PS3, there's
Gravity Crash.
On PC, there is the nice
Thrust Extreme, as well as
the excellent but extremely hard
Gravitron 2. Gravitron 1 is also great. There's also a Thrust remake in Blitzbasic called
Thrust Deluxe, but I've never tried it out.
On C64, there's the two awesome cult classics that started it all:
Space Taxi and
Thrust. Thrust has keyboard control only, but that makes the controls very tight.
Well, there's also an official sequel to Thrust,
Thrust 2, but I think it sucks. Thrust 2 is actually a totally different game on
CPC and Spectrum compared to C64. However, even on those machines it still completely sucks.
One could also argue that games like
Virus/Zarch,
Zeewolf 1 and 2 and
V2000 fall into the same category, because the player constantly fights against gravity. Those are 3D games though, and as such they feel quite different to me.