I remembered that Riot Zone/Crest of Wolf has limited paralax. There might be some in the elevator, & then there is atleast one scene outside in the 1st stage with scrolling buildings.
Also both Ys 4 & LOX 2 have some limited paralax.
Hell, Ys 1-3 have paralax, though, it's almost all choppy.
Anearth Fantasy Stories has some nice line scrolling in the battle scenes.
I've heard Blood Gear has some really nice paralax in some segments, but, I havn't played far enough to see. I wish someone would do a video of it.
Browning is another that comes to mind, lot's a paralax in that!
And who can forget Builderland!!
Cotton's first 2 levels have paralax, the 3rd has a static bg, & the rest is all solid stuff.
Super Air Zonk does have some limited paralax in a few area's, notably, the River stage, & the Moonhead stage.
Dragon Ball Z might have some paralax in it IIRC.
Exile & Exile 2 both have limited paralax in various spots.
Good grief, Genocide is loaded with it, however, that's not the only thing that game is loaded with
Horror Story has some some paralax in the first couple of levels
Jim Power has segments that are bombared by paralax...perhaps too much paralax, but, Dead Moon comes to mind in those sequences
John Madden is loaded with paralax, as the field uses line scrolling
Kiaiden 00, plenty o paralax
Popful Mail has limited paralax in teh first stage with the clouds
Psychic Storm has paralax, no doubt!
I think the first Ranma has some paralax
I think I also read that Sol Moonarge has paralax in some area's