What about arcade verts that aren't one directional or manic in anyway? Most of my fav's fall into this, from the transitional area started by Xevios.
Their is also Isometric shmups like View Point and Zaxxon.
Edit: Theirs also Caravan shmups. I'm guessing Inward moving shmups like Space Harrier don't count or is that what you meant by rails? Or did you mean arcade fps,s? aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Edit2:Also don't forget dmups, where you only dodge stuff like Barbie Super model or Sdmk. I hate me too.
I did great so much water and milk that I threw up when I was little.