Over ten years, the Friends gang spent most of their time with each other - including Thanksgiving, Christmases, New Years, Birthdays... at times, it was easy to forget that they even had other families! However, from time to time a parent, sibling, or cousin would pop up and make trouble - whether it was cousin Cassie (and Ross's wildly inappropriate behavior on her visit) or Phoebe's grandmother and her 'secret recipe' for cookies.
For the most part, the families of the Friends and their storylines were as problematic as the gang themselves (especially that of Chandler's father, who is a trans lounge singer in Vegas, and whose use on the show as the butt of jokes has been rightly criticized as being transphobic and inappropriate) - but there are a few family in there who were pretty decent people, too.
Best: Phoebe Abbott
Phoebe's birth mother, also named Phoebe, may be a little bit ditzy, but she's a good person overall. When Phoebe first finds out about her, she thinks that she is just a friend of her parents, and it is only later that she learns that the three of them were in a relationship together. However, when Phoebe got pregnant, she left the babies with Frank and Lily. She didn't realize for a long time that things fell apart with the Buffay family, and eventually she and Pheobe (Buffay) became close, and she even met Frank Jr and his wife.
Worst: Nora Bing
At first, it seems like Nora is the definition of a cool mom. The rest of the gang love it when Chandler's mom comes to stay, as she's a whole lot of fun and a famous erotica author. However, it's soon clear that she's actually a pretty terrible person. She makes her son deeply uncomfortable, and refuses to really act like a mother around him. She makes out with his friend (Ross), she involved him since childhood in her vicious divorce, and she makes transphobic comments to her ex when they are at Chandler's wedding.
Best: Frank Jr
When Phoebe first meets her half-brother, Frank Jr, while looking for her father, it seems like they don't have a lot in common. Frank is awkward, a little bit creepy, and assumes that Pheobe is a 'hooker' when she says that she is a masseuse. However, it turns out that he's not a bad guy, just a little bit clueless - and over time, he becomes a fan favorite character. He and his wife Alice are incredibly sweet together, and he becomes a good brother to Phoebe. After all, she's a quirky person, too!
Worst: Leonard Greene
Rachel's father may have his good points, but overall, he's a mean person - and Rachel is actually afraid of him for most of the series. He is rude, arrogant, and he refuses to tip well, despite being incredibly well off (always a red flag!).
When Rachel tries to teach Joey to sail, it's revealed that when Rachel was younger, her father would yell at her and berate her until she was near tears - and it seems like this continues into adulthood!
Best: Gloria Tribbiani
Joey's mom doesn't show up often, but when she first popped up, fans fell in love with her instantly. She is cheerful and loving, taking care of her (huge) family and always bringing Joey food, but that's not why she's such a great character. Fans also loved her reaction when Joey found out that his father was cheating - which was that of course, she already knew, and she was fine with it. In fact, she thought it was good for his father, didn't particularly care, and was most annoyed that her son thought she was so clueless that she wouldn't know in the first place! She's practical enough to figure out an arrangement that works, and to be both direct and loving when telling her son that she's a grown woman, and she does not need her kid looking out for her!
Worst: Jill Greene
Both of Rachel's sisters are pretty terrible people, but Jill is the better of the two... by a slim margin. She appears a couple of times across the series, always ready to gossip with Rachel and look for sympathy about being cut off for ridiculous spending. In some ways, she could actually be just a fun sibling to Rachel, except for her behavior around Ross. When she was visiting, she had no interest in Ross... until she learned that Rachel didn't want her to date him, at which point, she tried to seduce him just to prove she could!
Best: Sandra Greene
Rachel's mother is definitely the best member of her immediate family - even if she is far from perfect! She's warm and friendly, and while she can be overbearing and tends to criticize Rachel, when Emma is born, Rachel realizes that she needs her mother after all.
It's also nice to see that from the start, Sandra does have Rachel's best interests at heart - when the gang are trying to keep Rachel's parents apart for her birthday, and Ross seems like he has the same habits as her father, Sandra is there to gently call her daughter out. She's also kind to Monica about her 'boring' party, when most people are just plain mean about it. As far as mothers go, Sandra seems like a pretty loving one.
Worst: Amy Greene
Of the Greene women, Amy is by far the worst - and the most self-centered. She pops up in Rachel's life a few times, showing that a) she cannot Ross, despite knowing him for years, and b) she has no interest in anything that isn't about her. She pierces Emma's ears as a baby without Ross and Rachel's permission, she hopes that they die so that she can have a 'movie' experience of rising to the occasion of caring for her, she doesn't bother to learn her niece's name, and she is having an affair with a married man. Lovely.
Best: The Gellars
Ross and Monica's parents are surprisingly lovely, and have the biggest role of any parent on the show. Jack and Judy may have their flaws (like criticizing Monica more than Ross, or not quite knowing what is appropriate to say), but they are loving, and care about each other and their children deeply. They are also hilarious - Judy's responses to everyone in the gang during that fateful Thanksgiving where Rachel put beef in the trifle is one of the funniest scenes in the show, and the pair have some truly hilarious lines throughout.
Worst: Ursula Buffay
Could there be a worse sister than Ursula? Phoebe's twin is just plain terrible, and there's not a moment on the show where she is seen being particularly good to anyone (it's a mystery why Joey dates her). She doesn't bother telling Phoebe about their birth mom, their correct birthday (she actually got rid of Phoebe's birth certificate and can't her middle name), or their mother's final note to them (which is now lost). She lies to everyone, about everything, is flat-out mean, and illegally impersonates Phoebe. No wonder Phoebe just gives up on her.