A fuckton of games use transparencies, but many do for some minimal thing so they are not too noticable (for ex. the explosions in Saturn Bomberman are transparent too I think).
Try playing Cotton Boomerang, the game has a lot of (true) transparency effects.
For 3d the most the Saturn can do is clever manipulation of the backgrounds. The Saturn can't do transparent polygons. The best it can do is either a transparent ground field (using the VDP2 RBG), or to mix up 2d transparent sprites into a field of 3d polygonal graphics. The ground effect was done in Panzer Dragoon Zwei and probably Saga too (been a while since I played it), the sprite thing was used in Burning Rangers for the explosion effects mostly.
Even for 2d, transparency effects needed a lot of cpu cycles so few games could implement them in an impressive way.
I think Cotton Boomerang is the most impressive example I can think of. See:
http://evilboris.sonic-cult.net/SSF/Cotton_Boomerang_(J)/00000268.png
That's 2 backgrounds (the clock and the mists), a sprite layer (the flames, the witch), and another background (the clouds) - placed on top of the whole thing. All transparent.
ExCyber said:
I think that thing about "real" transparency on Genesis is wrong. Most likely that is pre-drawn; I've seen the same method used on a couple Neo-Geo games.
Could be just shadow/highlight effect. Which is transparency, in some primitive way.