Phoebe Buffay may seem like a charming, quirky, creative woman who would be all kinds of fun to hang out with, but the Friends' resident hippy chick was actually a pretty terrible person, sometimes. Sure, she could be warm and caring, but she had a tendency to lie and manipulate when it suited her, and she definitely took a lot of pleasure in making fun of her friends and putting them down. She was incredibly high-maintenance (for a woman who claimed to be the opposite), and she often acted childishly.
However, we can forgive her most of this - she had a tough life, and she often makes up for her worse qualities with how much she loves her friends, how much she tries, how much fun she is to be around, and how devoted she can be. Still, the times that she is the absolute worst are when she's not just a bad friend, but a total hypocrite.
The Fur Coat
One of Phoebe's biggest moral stances in the show is her vegetarianism and her passion for animal rights. So when she was gifted a fur coat, she was furious, and made a big deal of wondering how anyone could wear such a thing... until she put it on, realized it looked good, and started wearing it. This on its own isn't what makes her a hypocrite, though, as she actually struggled with wearing it due to her beliefs, and ended up giving it away. What makes her a hypocrite is that she flipped out over fur... but later on wears leather jackets, suede, and in her baby shower episode, is gifted leather pants (that she always wanted). If she refuses to wear animal skin for fashion, that should extend to leather, surely?
The Meat-Eating
Another aspect of Phoebe's vegetarianism that comes under fire is her refusal to eat 'any food with a face'... except when she does. The most obvious example of this is when she eats meat while pregnant, but like her fur coat, she struggles with this, and only does so because she trades off meat-eating with Joey until her cravings pass. However, she's seen eating meat in a few scenes, most notably when she is eating a lasagne with Monica early on. This could be considered a continuity error, rather than a moment of hypocrisy, but it wouldn't be totally out of character for Phoebe to self-righteously eschew meat... unless she really wants it.
The Job At The Spa
In the early seasons of Friends, Phoebe has a job as an independent masseuse, which suits her character perfectly. However, in later seasons, it's revealed that she took a job at a chain spa - which also makes sense. She's still doing the job she loves, but she has security, better pay, and benefits. The hypocrisy comes in when she tells all her friends that she hates chain spas because they put independent workers out of business, and flips out at Rachel for wanting to use a gift certificate at the place where she herself works.
The Smelly Cat Saga
This is a situation that fans can be somewhat sympathetic to - after all, it can be hard for any creative person to draw the line between 'selling out' and 'being successful'. But Phoebe clearly struggles with this line, especially when it comes to Smelly Cat. She ends a friendship with Leslie, her old singing partner, because Leslie uses the song for an ad jingle - and Phoebe claims that she was 'screwed over' by Leslie, even though she told her she could use the song (but it would cost her the friendship).
It's surprising, considering that she asks her audience for money for the song, and that she jumps at the chance to have it produced professionally, even with someone else singing. It seems Phoebe wants money for her songs, but considers jingles beneath her.
The Stolen Cat
One of Phoebe's most outlandish storylines is when she picks up a random cat that wanders into her guitar case, and promptly decides it is the reincarnated form of her mother, leading to her stealing the cat. When Ross (reasonably enough) calls her out on this after he finds missing posters for the cat, she gets angry, telling him to 'just be supportive'. When it comes down to it, though, she's not particularly supportive herself. For example, when her brother reveals he wants to be with his much-older home ec teacher, Phoebe sneaks around to try and break them up - why couldn't she 'just be supportive'?
The Wedding Charity
Phoebe has a difficult relationship with good deeds throughout the show - not only refusing to believe that a good deed can be truly 'good' unless it's 'selfless', but later struggling with whether or not she should donate the money saved for her wedding to charity. In the end, she goes back and forth - not just donating and then asking for the money back, but despite her earlier need for good deeds to be 'selfless', she wants the donation to be listed publicly under her name.
The Restaurant Showdown
Phoebe definitely has some double standards, and one of her most obvious was at her birthday dinner. In this episode, Phoebe has a reservation at a restaurant, but when all her friends are late, she keeps being pushed to smaller tables and feels humiliated by the wait staff.
It's not a fun situation, but it doesn't excuse her screaming at them when they do show up, and making a huge deal of how important it is for them to show up, on time, and stay for dinner for a friend. Of course, immediately after she gets a call from Mike, and bails on the meal herself. At least with this one, Phoebe knows she is being a hypocrite.
The Friends-Come-First Declaration
Another time that Phoebe's hypocrisy reared its head over a guy is when she flips out at Joey for canceling their plans. Just like on her birthday, Pheobe absolutely loses it at Joey when she learns that he wants to cancel plans with her to go on a date, berating him for putting a potential relationship above their friendship. So far, so reasonable (friends should come first!), but when she learns that David is in town for one night, she decides that rather than just talking to Joey, she will stand by her original statement... and then rush through their night together, ditch him, and head off to her own date.
The Pottery Barn Fiasco
Phoebe likes to make a big deal of how she hates chain stores, chain spas, really anything that isn't entirely original. That is, until she wants something from them, like a job at a chain spa, or a lamp from Pottery Barn. In one of her better-known moments of hypocrisy, Phoebe gets upset at Rachel for buying a bunch of Pottery Barn furniture for their apartment (and telling her it was from a flea market) - but then she sees a lamp in the window of the store, and decides to buy it herself. Once again, she seems aware that this is hypocritical, making Rachel pretend that she will move out unless Phoebe buys the lamp, but that doesn't make it better.
The Running Partner
One of Phoebe's defining traits is that she's quirky, and she doesn't care what anyone thinks. She even has a whole story arc around going running with Rachel, where she embarrasses her friend by running with her arms and legs flailing... and makes a big deal of the fact that Rachel shouldn't care what people think, she should just have fun. Like Phoebe, who clearly never cares what people think. Except, of course, when she does. Like when she goes to meet Mike's parents, and is so concerned about what they will think that she puts on a completely different persona, right down to her accent. There's some sympathy for her - meeting the parents can be intimidating - but for someone who makes such a big deal of not caring, it's not the only time she clearly really cares.