It was more of an arcade sim, but noting beats the raw talent needed to fly exclusively from first person in the Amiga classic, "Wings!" I LURVED that game...classic joystick, epic battles, being able to save my game...forgetting to save my game. T_T
Plus, there were top-down "Barnstorming" strafing missions- a WWI shmup, AND a WWI dog-fighting sim. It does not get much more classically awesome than that.
...and thanks, Aviadmd- I can't believe I forgot all the hours I logged on Wing Commander: The Secret Missions. Another ridiculously fun game.

Ugh. Suprisingly hard question. For just flight-flightsims, IL2 Sturmovik sure. If you broaden to space sims, it gets harder. Freespaces and I-Wars. And if you go for more arcadeish, Crimson Skies. So many to choose from, but I'd have to say ... *drumrolling*
Freespace 2.

Got to say its a 3 way tie for me-
*Freespace 2
*TIE-Fighter
*Wing Commander 3
O' and IL2 Sturmovik hands down for Airplane Flight Sims

Oh, and I kinda forgot to mention the Elite series! (Preferably the Amiga versions)

Starlancer,

Freespace 2.

I was always partial to Psion's "Flight Simulator" on the ZX Spectrum Link.
Small "World" area. Cessna-type craft. 2 runways. Several navigation points, but you take off, fly around, land with nothing telling you what to do (missions) or go to point xx,yy.
Spent many an hour on this in my youth.

Looking Glass' Flight Unlimited was a blast, and something different to most of the flight sims out there.
Also, I'm glad someone else has mentioned LHX Attack Chopper already. Also great fun.

IL-2 Sturmovik

Freespace! :D

Eugh, my heart says TIE Fighter. However for sheer amount of time played it would be F-19 Stealth Fighter.

Given that you're counting it as a flight sim, I'll opt for Freespace 2.

F117-A Stealth Fighter

IL-2 Sturmovik for me.

Well, if I can add space-flight to the flight sim genre, I'd say Privateer. If not, hmm... then I'd have to say the first A-10 Tank Killer by Sierra. Man, do I feel old now, lol.