Does the 2nd printing of Deities and Demigods have Cthulhu? I have heard that it does, and I have also heard that it does not. Does it or not?
Actually, and technically, Yes. The second printing DOES contain those two mythos. It is every subsequent printing that does not contain them.
For the first 1980 printing, TSR obtained permission from Michael Moorcock for inclusion of Melnibonéan material (from his Elric series of books). The Cthulhu Mythos was believed to be in the public domain, so TSR assumed they could legally use it without any special permission. However, Arkham House, who held the copyright on most Cthulhu books had already licensed the Cthulhu property to the game company Chaosium. Furthermore, Chaosium had also licensed the Melnibonéan copyright from Moorcock. When Chaosium threatened legal action, the first printing was halted and the two companies agreed on a compromise: TSR could continue to use the material but must provide a credit to Chaosium to do so. TSR added the credit for the second printing of the book.
The Cthulhu and Melnibonéan mythoi were removed from the 1981 edition, making it a 128-page hardcover (and giving the original edition a high collector's value). TSR felt its material should not contain such an overt reference to one of its competitors and removed the two pantheons altogether, thus negating the need for the credit. For this reason, the first and second printings have generally been in greater demand by D&D fans and collectors.
So, as you can see, both the first AND second printings contain them. The second printing contains a note giving credit, where the first printing does not.
You DID ask about the second printing specifically... and just because the first printing was halted AFTER being issued, this does not invalidate the fact that it was a first printing.
EDIT this is from someone who bought one of the original first prints in 1980, and got to see one of the second prints when a friend got his.
I was just looking at my husband's Deities and Demigods book and have the two pantheons that are missing my printing is may of 1980. It also has the credit to chasoism for the use of those two pantheons. So, I am assuming this is a second printing. Now I have to decide what to do with his gaming books as he has passed and I haven't played in years. To all you gamers out there have fun and enjoy.