Hexen

Same list as in the original Doom:
All of the static 2D screens (like the between-level maps and title screen) are pillarboxed, and the automap is hor +.
The HUD stays centered, and a stone background appears to the left and right of it.
The text screens that appear at the end of each episode have the tiled background expand, while the text remains in the center of the screen.
The cut-scenes that follow, which are really just sparsely animated 2D backdrops, are pillarboxed.
High aspect ratios, sadly, don't work so well.

Extra anomaly: It is playable in GZDoom, but it has an interesting bug. This is the first game using the Doom engine where some of the weapons are oriented to the side instead of the center. This can produce strange effects for these weapons, like a disembodied floating arm, or a swinging axe coming out of nowhere.