The amount of physical trauma that any given Addams undergoes would put Homer Simpson to shame. Just in the two movies we see Pugsley get electrocuted, a cannonball fall from the top of the house onto Lurch's head, Pubert survive a multi-thousand-foot ascent and descent, and Gomez and Fester tossing each other around like they were rag dolls. To any normal human any of these would be instantly fatal, but the Addams shrug them off like rainwater. Beyond that, there are countless instances of the Addams's attempting to kill each other — sword fights, knives being thrown at one another, a mobile of daggers hanging above a baby's cradle — but mysteriously all of them fail to hit the mark. All of the knives just barely miss and nobody suffers a scratch during a sword fight. It's entirely probable that Grandmama has been putting poison into the Addams' food, knowing that none of them will die. It's therefore become something of a challenge within the Addams clan to see how far they can push each other, to see exactly what it takes to hurt or kill an Addams. When Gomez throws a knife at Fester's head, he's actually trying to hit him but the curse is making the blade just barely miss him.

When Debbie (the "black widow") marries Fester in Addams Family Values, she makes multiple attempts at killing Fester and fails every time — because through marriage, she's now an Addams. It is impossible for her to injure or kill Fester. She doesn't understand this, however; she's a murderer and isn't aware of the Addams "curse" in this matter. And in the finale of that movie, note that none of the Addams were particularly concerned while they were tied up; they treated it largely like an interesting experiment. Pubert didn't actually "save the day", he was just playing his role.

"But wait," you say. "Debbie was actually killed when Pubert crossed the wires. Therefore, an Addams can kill an Addams."

Not so. In the movie you see Debbie throw the switch, Pubert change the wires, and the current return to Debbie. This was an act of gratuitous editing. If current was running through the wire, it would have stopped running once Pubert unplugged it, then started running again when he plugged it back in. That didn't happen, so we know that Pubert couldn't have unplugged and plugged after Debbie threw the switch. Furthermore, electricity through a wire travels at about 6.7 million miles per hour. It's therefore impossible — even for an Addams — to switch up the plugs the way Pubert did in the time it took the surge to go from the switch to Pubert. Therefore what actually happened was, Pubert changed the wires and then Debbie threw the switch. That being the case, Debbie committed suicide and suicides are not protected by the Addams curse.

"So then why did Debbie fry, but Pubert shot himself 30,000 feet into the atmosphere and landed without a scratch?"

Intent. Debbie had murder in her heart; Pubert did not. The curse accounts for that. Pubert wasn't trying to kill himself, he was trying to play his part in saving his family.

"But what about all of the Addams's in the graveyard? What about Uncle Knicknack in the attic?"

We never know what happened to Uncle Knicknack, but given his state (stored in a bag in the attic, not given a proper burial) it's reasonable to assume that he suicided, and it's likely that in the Addams clan suicides are seen as a coward's way out. Therefore, Uncle Knicknack was never included in the graveyard amongst the "honored dead" because he dishonored himself by suiciding.

And as for the graveyard, all of the residents there have backstories that put their cause-of-deaths to people and events outside of the Addams family; Wednesday's great-aunt Calpurnia was burned as a witch in 1706, Aunt LaBorgia executed by a firing squad, etc. All killed by people outside of the Addams family.

Furthermore, in the first Addams Family movie we see evidence of this; during Tully's second sword fight with Gomez, he (Tully) scratches Gomez's hand and draws blood, the only time we see blood drawn anywhere in any Addams movie or TV show. And when that happens you can easily see Gomez's who attitude shift; when the fight started he was as playful and madcap as he always is, but the moment Tully drew blood his whole demeanor changed to something more serious. He knew that he could actually be killed since Tully was serious and isn't family, and his attitude showed that understanding.

There was also a TV episode where a policeman paid a visit to the Addams house. Lurch patted him down and found a gun. Lurch was not happy about this and only reluctantly returned it when the man identified himself as a cop. Why would Lurch care if there was a gun brought into a house filled with blades, explosives, poisons, and who-knows what else? Because a non-Addams with a gun can actually kill an Addams. Lurch was concerned.

"Yeah, what about Lurch? He's not an Addams."

Lurch is timeless. He's been the Addams' butler for hundreds of years and was around when the curse was first laid on them; therefore he shares the Addams' durability. When the last Addams family member dies, the curse will be lifted and he'll likely turn instantly to ash.

In the musical, Wednesday falls in love with Lucas Beineke, but due to his lack of "adamness" she rejects him. In order to prove that their love is legitimate, Lucas convinces Wednesday to fire a crossbow at him while she is blindfolded. He specifically says

"We're connected you see? We're destined to be together! So nothing bad will happen."(Act 2 Scene 6).

When, she fires the arrow, the arrow is guided along by the ancestors and misses him, maintaining the curse that an Adams cannot kill an Adams.

See, Wednesday and Lucas's marriage has already been decided by fate, more specifically by Fester who is shown in the play to break the fourth wall, but that has a whole bunch of other implications. Therefore it is impossible for him to be injured or killed by Wednesday.

Not exactly sure if the Broadway musical is considered in the same universe, but I'm was playing pit orchestra for it and the play is so ingrained in my head that I immediately made this connection.