There are only a few things that can kill demons in Demon Slayer. The most common methods are exposing them to sunlight or decapitating them. The latter is often used by the Demon Slayer Corps, but plenty of demons have found workarounds to avoid this manner of death.
In order to cover all the demons who have survived beheading, a few rules will be observed. Beheading, or decapitation, refers specifically to the act of cutting off the head of a demon. Therefore, demons who have their heads destroyed but not cut off like Yushiro won't be counted. Near-deaths by decapitation like Akaza's also won't be counted as chances are if their heads had been properly cut off, they would have died. Generally speaking, all demons can die when beheaded under the right circumstances, but these are the rare exceptions to that rule.
Demon in the Temple
This is one of the first-ever demons Tanjiro encountered. It happened at the start of the series before he was even inducted into the Demon Slayer Corps. Nezuko managed to remove the demon's head by kicking it off, but since she didn't use a Nichirin Sword, it survived.
What's funny about this one is that Urokodaki, the man who went on to teach Tanjiro how to kill demons, gave the strangest form of advice. He told Tanjiro stabbing the head won't kill demons and made him come up with another solution. Tanjiro concluded that he had to crush the demon's skull with a nearby rock. He faltered long enough for the sunrise to kill the demon, but it's funny how Urokodaki ever let Tanjiro believe that this was an effective strategy. He might have just been testing the boy's resolve, but he should have at least loaned him a sword.
Spider Demon (Elder Sister)
This is another situation where a Nichirin Sword wasn't used to deliver a killing blow, so nothing came of it. This demon had her head removed by an angry member of the Twelve Kizuki, Rui. However, as Tamayo explained earlier in the series, demons fighting each other is pointless; since neither of them can use a Nichirin sword or sunlight, neither of them can deliver a decisive, killing blow.
The fact that demons can't kill each other made Rui decapitating his sister a simple act of cruelty. He knew he couldn't kill her, but he could still inflict as much pain as he wanted in order to keep her in line and make her fear him. However, this is not how a family should work, or any relationship for that matter. Tanjiro called him out on this, but Rui's only response was to try and steal Tanjiro's sister for himself.
Rui
Rui's survival method was one of the most annoying in the series considering how it's set up. It came when Tanjiro used a combination of the Hinokami Kagura and Nezuko's explosive blood to slice through the Lower Sixth Kizuki's abnormally strong neck. Not only was it the most beautifully animated scene of the series up to that point, but it had a lot of emotional weight behind it as Tanjiro finally proved how powerful the bond between him and Nezuko was.
Unfortunately for Tanjiro, Rui survived this epic climax to their fight. According to him, he was able to cut his own head off with his threads before Tanjiro could do it himself. This invalidated Tanjiro's victory, and also cheapened the effect of one of the most impactful moments in the series. None of this matters anymore though, since Giyuu came in to finish him off.
Enmu
Enmu provided an interesting means of surviving his decapitation. It came up during the "Mugen Train" arc of the series. Here, Tanjiro found and confronted the demon on top of a moving train. Enmu tried to use his Blood Demon Art to put Tanjiro to sleep, but Tanjiro found a way to wake himself up immediately. After several cycles of Enmu putting Tanjiro to sleep, Tanjiro waking himself up and approaching Enmu, the boy was finally able to slice off the demon's head. Or so he thought.
As it turns out, what Tanjiro was fighting wasn't Enmu's real body. While Enmu had Tanjiro and the other members of the Demon Slayer Corps caught in a deep slumber, he merged himself with the train that they were all aboard. In order to kill this demon, Tanjiro would have to find out where the demon's real neck was and cut him there.
Daki
It seems that most of the members of the Twelve Kizuki have special means of avoiding decapitation by a Nichirin Sword, so it's natural that Daki, the Upper Sixth Kizuki, would also have a few tricks up her sleeves. In her case, it's her Obi Sash. Daki's Blood Demon Art not only allowed her to produce and manipulate several Obi at once, but it also apparently let her body take on the properties of an Obi. When Tanjiro's Nichirin Sword made contact with Daki's neck, it seemed to make her head roll, but this was revealed to be wrong. The truth was that her neck, having taken the form of one of her Obi, was able to bend and weave like a cloth in order to lessen the impact of the blade so it wouldn't go through. Tanjiro would have to cut much faster and harder in order to succeed.
Nezuko
Nezuko was the latest to survive decapitation in the anime. She's not a member of the Twelve Kizuki, but she apparently has power that puts her on par with the Upper-Rank members. This may have something to do with being turned into a demon directly by Muzan, though that remains to be confirmed.
Nezuko's ability to keep her head attached to the rest of her body was revealed when she confronted Daki. When the Upper-Rank Sixth used her Obi to slice off Nezuko's head and several other body parts, she was able to manipulate her own blood to keep everything connected. Technically, this wouldn't have worked anyway since Daki is a demon. However, it stands to reason that if Nezuko were for whatever reason to go up against a member of the Demon Slayer Corps, she could pull the same stunt to keep a Nichirin Sword from killing her.
