I have always called them scrolling shooters since that is what the gaming publications of the day called them (single screen being Space Invaders type), then with the rise of First Person Shooters, scrolling (overhead, side) shooters became more prominent. The genre kind of died off with the PlaySatation console as we transitioned into the next gen with PlayStation 2.

I personally enjoy a good scrolling shooter. They can be quite fun if programmed well.