Of the main villains of the games, the ones to ultimately be killed off are: Grand Battle Kukku 15th, Black Doom, SCR-HD/Master Core: ABIS, Captain Whisker, Mephiles, Iblis, Ifrit, Eggman Nega (unless he somehow gets out of the Ifrit's dimension), Dark Gaia, Metal Sonic, Time Eater, and the Deadly Six. But with all of the following, people think they survived:
Black Doom - Status bar is listed as "Unknown" instead of "Presumed deceased", even though it also says "He hasn't appeared since and is most likely dead". This is the mildest instance of this. The basis on which people think he survived is probably a.) His claim to be immortal (but at the same time he's shocked at his defeat, probably shock at how he can die while immortal), b.) Metal Sonic survived a similar defeat in the previous game.
Captain Whisker - Before I did a little research, it said "His fate after Ghost Titan's defeat is unknown". But the game has Blaze speculate that the Jeweled Scepter "sunk with the pirates", and when Eggman and Eggman Nega are the threat, it's said "The pirates are gone, so who could it be this time?" (Note: I might not get the quote exact) So the game confirms Whisker was killed in Ghost Titan's explosion and sinking of his ship, since they never considered the possibility that he survived.
Eggman Nega - No one's but me has given any speculation as to his fate after being trapped in the Ifrit's dimension, but if anyone thinks he's still alive somehow, this one would actually make the most sense seeing as how he escaped his fate in the previous game, and Eggman escapes a slightly similar fate for no reason between Sonic Generations and Sonic Lost World. For those reasons I haven't even tried listing the possibility of his death on this wiki outside of blogs and comments, knowing I'd receive numerous arguments if I did.
Dark Gaia - Sonic smashes through his center eye, he falls rapidly decaying, gushing green blood as he falls back into the lava. Now I know the lava won't kill him, he appeared from the lava earlier, but Sonic's attack did, and he was the only Sonic character to make TV Tropes's FamilyUnfriendlyDeath list. But because of Professor Pickle's line about the balance of good and evil, people think he survived, much like Lord Darkar of an anime I know.
Metal Sonic - Aside from the possible doom of Eggman Nega, Metal Sonic is the only recurring character to be killed, all other bosses listed above being one-time. Classic Sonic kicks him and he explodes. Not "explosions appear on him and he survives", like we see in plenty of games, but actually explodes. And is not present during the final battle. But because he appears in the white space afterwards, people think he survived, even though any instance of Sonic revisiting a stage he's been to before is probably non-canon, it's just there so the player can play it again any time he/she wants.
Deadly Six - I did an entire blog about that. When defeated the first and second times, they simply jump away. When defeated the third time, Zazz, Zomom, Master Zik, and Zeena explode, Zor and Zavok fall into lava. But because Eggman tells Sonic he'll control the Deadly Six again after his final defeat (as well as Zeena saying she'll feed Sonic to Zomom despite Zomom being dead at this time) people think they survived, that the Deadly Six can teleport (which they haven't demonstrated the last two times) and survive lava (which Zor's line suggests they can't, but many are inclined to dismiss his words due to how pessimistic he is). I think either Eggman didn't witness the fights with the Deadly Six and assumed they escaped a third time (same with Zeena), or else he was planning to revive them using Chaos Emeralds. (This is only the Wii U version, in the 3DS version they survive, or so I heard, they simply fly away instead of exploding or falling into lava)
Which leaves the only main villains this wiki truly considers dead: Grand Battle Kukku 15th, SCR-HD, Iblis, Mephiles, Ifrit, and Time Eater. (Does Time Eater count as a main villain, seeing as how he was working for Eggman the whole time? Well, if Captain Whisker counts, so does he, right?) I guess plenty of people think Eggman sets an example for the villains since he survives countless defeats which the ending of earlier games implies that he is dead but he always returns. But he's Eggman, he's like the Sonic equivalent to Bowser, and now that they've had him for so long, they can't permanently kill him off unless they make a chronologically final game, as opposed to one-time villains like everyone listed above except Eggman Nega (which is most debatable) and Metal Sonic (which did come as a shock).
Then again, this could just be coming from one who's really into villain defeats