The first production EA games all came in cardboard boxes, Madden, Zany Golf, Budokan, Block Out, Road Rash, etc. Then they started using plastic. Balistic/Accolade used cardboard boxes as well, until late, Winter Games, SUmmer Games, Onslaught, Hardball, Star Control, etc. Most all the other third party, as well as Sega used plastic. And yes it was a cost saving deal to switch to cardboard. I personally prefer the pastic, I don't know why anyone would want cardboard if you also game, it will degrade opening and closing. As a collector, I just want to be able to find them complete, and in good shape.
I have seen some cardboard versions of some games, that came out prior to 94, I believe so anyways. Some do have multible releases,
Barbie Super Model, World Of Illusion, etc. World of Illusion is a black box, kind of odd seeing a black box genny game, and not be plastic.

But some titles were released, as plastic, and then when the swap happened they went to carboard. Others were cardboard only late releases:
Shining Force II
Phantasy Star IV
Sonic & Knuckles
Sonic 3D Blast
Ristar
Vectorman 2
Mega Bomberman
X-Man 2
Some sports titles
(I think most of those were anyway)
Also of note, was the Majesto(sp?) releases, these were a TON of these at TRU and from Amazon online even until last year. They re-released the Genesis 3, as well as several Sega games, and I think they did Frogger, themselves, all of their releases are cardboard.
One thing also with the cardboard releases, budgets one, anyway, most have B&W instruction manuals, just another cost saving measure.
Oh and I have the Sega Classic version of Golden Axe, this too is a late re-release by Sega, it'd dated 95, but it's in a plastic case! So it's very odd the way they flip floped around with all these different versions. I always loved the Sega cases versus cardboard of NES and even the old Atari. Just so much cooler!