The game I'm thinking of was made for the earliest windows versions.

Gameplay: Spaceships came down from the top of the screen, and to shoot them you had to type a word on the screen.

Could anyone help me find the name of this game?

I don't know the game, but google "type speed games" and you'll end up with a bunch. Perhaps someone already did a remake that can lead you to the name. Good luck!

Was this an old form of typing tutor? If so it might be "typing invaders" - a version of space invaders rigged over to typing words and letters

However the underdogs website might also contain the answer and possibly the game itself.

http://en.wikipedia.org/wiki/Home_of_the_Underdogs

http://www.hotud.org/home

Similar to that typing invaders, but the words were under the cannons and not really meant to learn to type, very simple game and very old.

The description reminds me of Space Invaders, I miss playing that game. I found Word Invaders, which is cool because it teaches you how to type at a fast pace as the levels increase.