What are some good games where you fly forward and you shoot enemies in front of you?
Especially those ones, which where made for the 2D hardware.
>inb4 Space Harrier
...and where you're not a running man.
you may enjoy Hyper Zone for the SNES.
two more than have fun fly-behind segments on the NES:
Flight of the Intruder
MiG-29 Soviet Fighter (though this game was on a bunch of euro-consoles as well)
"Metal something-or-other 2"
I really can't remember the name, but you were a squad of guys in power armor and would blow away hoodlums as you scrolled through a city. It was actually a sidescrolling lightgun game, though.
Because it's by a Spanish developer, was released in a time of polygons and not in America. You might, just maybe have heard of Biomechanical Toy, a run'n'gun by them.
Check out Gungage it's like these type of arcadey games except with limited exploration and unlockable characters.