Time Pilot by Konami, arcade release in 1982.
Sigh. those old Atari and Colecovision boxes really take me back, they just don't make 'em like that anymore! "Plays like the real arcade game!" Liars! It never did. Well, I guess Time Pilot sort of did. I remember being equally awestruck with fascination as a kid, going to Fun 'n Games arcade and playing all these uprights - then wandering into Child World or Toys R Us and seeing all these shrink-wrapped boxes in the special plexiglass room they stored them in, all piled up, of the console versions of these games - and just wanting to take them all home with me.
Time Pilot was a unique little shooter in its day. It still has an endearing presentation unlike many other games - you control a little screen-centralized, free-flying craft which will rotate (and aim) in any direction you point it, and the screen will scroll accordingly. Sharing the screen with you is (surprise!) various targets for you to shoot, or be shot down by. Make your choice!
Additionally, you must rescue parachuting pilots for bonus points (say that 5 times fast!) and take out moherships to advance rounds. Especially for the time, this was a pretty busy game!
The wikipedia entry on the development history of this is interesting, noting that the original designer's proposal for the game was rejected and that he was instead tasked with making a driving game. Not being too hip to that idea, he and his programmer created Time Pilot in secret, and when it became successful, his boss took credit for the idea. Dick! Anyway, don't feel too bad - that original designer is Yoshiki Okamoto, who went on to see great success at Capcom with several popular titles, and has since lead his own development studio Game Republic. (his "symbol," the Yoshiki, can be seen in many earlier Capcom games appearing as a very useful powerup)
Make sure to download Headcase Games' original release of iFist while it is still FREE for the holidays!