what are each world champions favorite opening?

I think I said this in another thread, all players after Fischer were universal, but even with that in mind most of them have a favorite opening.

I dont know much about Morphy, but he seemed to love the Evan's Gambit.

Steinitz was an interesting subject, early on in his career he was called the Australian Morphy for his attacking style,  a lot of his games when he was young feature the Vienna, but then in his older years he developed a lot of ideas in the Queen's gambit and also studied the Ruy Lopez with restrained center, I think he was the one that came up with Nbd2-Nf1-Ng3.

Fischer's favorite openings were the Najdorf/KID.

Kasparov's openings were pretty much the same as Fischer. Altho we have to mention he loved the Scotch and in his early years played 1.c4 as his coach, Botvinnik(Fischer mostly played the Ruy Lopez)

Karpov played about anything, but I think he favored Queen's Pawn openings.

I dont know about Botvinnik or other World Champions, Botvinnik developed the f3-e4 idea in the QGD Exchange but that does not mean it was his favorite opening, probably his favorite opening was the English.

You can find the most played openigns of a player in chessgames.com, some examples:

http://www.chessgames.com/player/emanuel_lasker.html

http://www.chessgames.com/player/jose_raul_capablanca.html

http://www.chessgames.com/player/tigran_vartanovich_petrosian.html

After Kasparov it is quite hard for me to know Kramnik's favorite openings, he is well known for the Berlin Defense but he plays about anything, just as Anand and Carlsen.

Perhaps it would be of interest to consult Chess World Championships 1834–2004 compiled by James H. Gelo.

https://web.archive.org/web/20140708094050/http://www.chesscafe.com/text/cwc.pdf

With regard to Morphy, it would perhaps be of interest to explore how his match opening play differed from what happened in informal games.

"... Our hero had first move, and ventured the Evans' gambit, which he lost, ... Morphy was charmed with Anderssen's defence thoughout, ... It proved to him that the Evans' is indubitably a lost game for the first player, if the defence be carefully played ..." - Edge (1859)

Of course, that was the last of Morphy's important matches.

Looking at chessgames.com looks like the cheaper and therefore best option