Canonically Morticia is a witch. This has already been mentioned in FuzzyBoots's answer. The connection to witchcraft is never made explicit as far as I remember, though Morticia does magic, and then there is this passage in Season 1, Episode 5 of the original black and white series (MGM made the full episode available in Youtube):
Genealogist: "I've traced Mrs. Addams back to the early colonial days at Salem, Massachusetts. Interesting place, Salem. They burned witches there, you know."
Morticia: "Yes. I'm certainly glad they don't do that today."
Below are some spoilers for recent material on the Addams.
In the 2022 Netflix series Wednesday, both Morticia and Wednesday have visions of past, present and future. Wednesday attempts a séance without success, but at some points she is able to see, communicate and once even physically interact with the spirit of the very first Addams - all through her own powers.
In the Addams Family Values movie from 1993, Wednesday tries to decapitate Pubert with a guillotine. Pubert, who is not even one year old at the time, catches the blade with the tips of his finger. This is a display of superhuman strength and agility for his age, and possibly cunning as well.
I do not remember a single super human feat from Gomez in any live action media. However, in the 90's cartoon, there was an episode in which he is trying hard to fail at something. He shoots himself from a cannon and manages to knit a sweater during his flight while wearing a helmet two sizes too small. Despite punching a hole through the ground, the only thing he managed to hurt was his own pride.
Some small spoilers for recent material on the Addams below.
In the Netflix Wednesday series, he claims to have had multiple lobotomies, because they are "like tattoos and you can't get just one", and yet he is still - somewhat - functional. He is also able to produce electricity from his fingertips.
In the 1991 movie, he regains his memory after being electrocuted by a book. This, together with the spoiler above, are references to the original series, in which he claims to be able to produce 110V AC from his body, and proceeds to put his mouth where his money is.
The 1991 Addams movie ends with Fester taking Wednesday and Pugsley to a game of "Wake the Dead". Whether he is actually capable of doing so is left to the audience's imagination, but being the Addams he is, I don't doubt anything at this point.
In the cartoons, he also survived all kinds of hazards that would instantly kill a human. I distinctly remember how he loved to wear a suicide bomber jacket and blow himself up, though he would only get slightly charred from it (and oh boy that joke was horrible and wouldn't fly today).
He is also able to summon gargoyles:
I remember her being a witch and making potions here and there, such as in the first movie. Unfortunately I don't have much on her to be able to say anything else.
In the Addams Family Reunion movie from 1998, it is stated that Lurch is considered part Addams. This is because his heart came from an Addams, so I had to include him here. He is super strong, and has face of an IT worker (ok this joke is coming from me, not any author nor writer officially involved with the Addams).
In episode 32, season 1 of the original black and white TV series, Gomez mention that Itt Addams has an IQ score of 320. I simply don't know whether this is meant to be taken with a grain of salt - whether this is true is up to the audience's imagination. If true, however, Itt would be more than 13 standard deviations more intelligent than a regular person. This would make him smarter than anyone who has ever lived in the real world and most every fictional universe, even those with superhero scientists.
Itt is also able to make his gibberish understood sometimes only by his relatives, sometimes by other people as well, but never to the audience.