In the very first episode, Will has trouble getting on with the rest of the family - except for Ashley, who shows him her art, and is taught to rap by him.
One for a series as a whole, namely in the series finale that with all of the family moving to different parts of the country, Phil gets Carlton, Hilary and Ashley to agree to call himself and Vivian at least once a week on Sunday, and as Phil leaves the house for the last time, he looks fondly at Will and simply says "Sunday."
That entire episode was heartwarming. Every interaction Will had was closure and love. Especially when Phil tells Will that he is his son, because Will wanted a father throughout most of that series, and the one time that his father did appear led to one of the biggest Tear Jerker episodes of the series.
Uncle Phil: You are my son, Will. End of story.
This line deserves recognition as it reveals that despite their rocky relationship, Uncle Phil always thought highly of Will
Uncle Phil: You don't know my first memory of you. I remember, the kid loaded with all the potential in the world. Now I see someone on the verge of realizing that potential.
Will joining Carlton in dancing and singing to "It's Not Unusual" by Tom Jones. This is especially heartwarming, since he was shunned for the song, and that in the end of the show's run, Will joins in.
On that note, here's a meta-example: This surprise reunion of Will, Jazz and Carlton, which also doubles as a Crowning Moment of Awesome. In case the link doesn't work properly, skip to 1:38 for pure awesomeness.
Uncle Phil calling out Will's father for abandoning him again was this as well as a Crowning Moment of Awesome. For all his annoyance, Phil really cares about Will.
Also from the finale, Hilary snottily demanding that Geoffrey take her bags to the car. When he comes in, she reveals that she was just kidding and wanted to say it just one last time, only to have Geoffrey pick her things with a smile and say "It would be my pleasure".
Geoffrey setting up a poker night for 13 year old Ashley, when she can't go with the rest of the family to an event and feels left out. He sets up a full poker table and at first they bet cookies, when she says she still feels like she's treated as a kid he gets out his wallet. Ashley proceeds to wipe the floor with him. It's a nice moment from the usually snarky Geoffrey and shows that Ashley may be his favourite member of the family.
In "Bullets Over Bel Air", Everyone reacts their own way when it comes to Will getting shot. Props go especially to Hilary, while her demands at the hospital seem to be her snotty self on the surface. Inside, she just wanted to help her cousin out any way she can. Especially since for once it's not for her, it's for Will.
At the end of "Just Infatuation", Will watches Ashley doing her hair and smiles and we get a flashback of how, when he first came to the household, she was the one who liked him first despite his antics clashing with her family. Will's been protective of her, as she was the youngest of the family, and she's growing up before his very eyes.
Also from the finale: In the first part, Geoffrey suggests to Phil that it would be a wonderful gesture to give him a first-class one-way ticket to London on the Concorde in lieu of his spring bonus. Phil, known for his thriftiness, tries to bargain it down. Then, at the end, Phil presents Geoffrey with a first-class ticket to London.
Geoffrey: In lieu of my spring bonus?
Phil: In addition to it. *presents Geoffrey with an envelope*
Also from the finale: Phil asks Will when Jazz will come by to pick him up; Will replies that he'll come as soon as Phil leaves.
Phil: (Laughs) Good idea... but when he comes by, wish him all the best from me.
At the end of "Hilary Gets a Life" (Season 2 Episode 39), Hilary's about to quit her first job as a caterer in tears. Geoffrey tells her that he raised her, and that "Geoffrey don't raise no fools", and gets her to pick up a tray and walk into the party like the Queen of England.
There was also one during the episode's family meeting. Ahead of complaining about needless expenses, Phil and Vivian congratulate Will for setting a fine example by getting a job and not being dependent on their money to buy things.
In the two-parter "There's The Rub", Hilary and Carlton volunteer at a local soup kitchen for Thanksgiving. They start out due to their own selfish desires: Hilary is promoting her show and Carlton wants a letter of recommendation so he can get into Princeton. However, after getting to know some of the residents of the soup kitchen and serving until they run out of food, they decide to give them a Thanksgiving they'll never forget. How? By hiring caterers to serve them a Thanksgiving feast.
A small one: in "Mistaken Identity", Bob who was established as a tough guy, starts to sing "One" by Three Dog Night in a heavenly voice when Will and Carlton leave the jail after being cleared, implying that he misses them.
In a Season Five episode, Ashley and her boyfriend are considering having sex; Ashley, a virgin, is confused and scared about the whole situation. She seeks out Vivian for The Talk, but she is attending a conference. Ashley is trying to figure out what to do when Hilary walks through the kitchen on the way to her show; though at first she claims not to have time to talk, her "big sister radar" informs her that Ashley has something important going on. The two sit down and share a tender scene, with Hilary sharing the story of her first time and offering Ashley some genuinely good, intelligent advice: she'll know when she's ready, and it has to be her choice, not anyone else's. She then tells Ashley that she knows she'll be fine, because she's always been intelligent and responsible, and promises to support her no matter what. It's one of the few times we watch Ashley and Hilary act truly sisterly on the show, and it's nice to see Hilary showing a deeper side than usual.
Carlton and Hilary trying to save a horse in the subplot of "I, Stank Horse" is pretty sweet, especially when you consider how the two of them tend to be.
After Hilary is asked to pose for Playboy, Phil flips out, of course. But by episode's end, he finally calms down and acknowledges, "You're not a little girl anymore. You're a beautiful woman. Beautiful enough for Playboy to ask, and woman enough to accept."
Hugh Hefner has one at the end. Phil in a bit of an Up to Eleven moment of craziness over the matter decides to join a monastery till the Playboy thing blows over. Will visits him and gives him the magazine, telling him he has to see it. Phil reacts squicky at first, but opens it anyway and finds out to his glee that they covered up anything on Hilary that would be revealing. Meaning that Hugh took Phil's feelings to heart after meeting him.
Phil and Vivian once appeared on an episode of Soul Train when they were younger. The scramble was supposed to read "James Brown" (notably, only the initials were swapped). Phil made it read: "Vivian, I love you and I always will. Marry Me?"
Another one from that same episode was Will (correctly) guesses Uncle Phil doesn't want to go on Soul Train because he's insecure about his dancing abilities. Rather than make fun of him, Will brings a friend of his over to help Uncle Phil.
A minor one in "Winner Takes Off", Geoffrey is celebrating winning the lottery (really a prank by Carlton and Will) by insulting the family. During it, he promises to buy Ashley two Mercedes after he wins. This really shows how close Geoffrey and Ashley are.
Also, when Uncle Phil learns Geoffrey quit because of Carlton and Will's prank, he shows no hesitation in letting Geoffrey come back despite all Geoffrey did after he thought he won and is understandably more mad at Will and Carlton than Geoffrey. Even though Phil can be stern this shows he's not unreasonable.
In "Home Is Where The Heart Attack Is." Will feels guilty about his role in Phil's heart attack. When he confesses to the family (sans Carlton who's at home in denial), they berate him for nearly getting his uncle killed, making him even more guilty. He goes to apologize to Phil, but Phil hears none of it, taking the blame all to himself from years of not taking care of himself. When he asks where Carlton is, since he was the only one that didn't show up in the hospital; a now absolved Will goes home to check, leading to the Tear Jerker moment.
A subtle moment in "To Thine Own Self Be Blue...And Gold" Will discovers his new boss (and Uncle Phil's friend from Princeton) wants him to deliver a bribe to a councilman so he can set up his new office. Will takes the suitcase and goes home to tell Phil. When Phil comes home and Will tells him he wants to quit, Phil gets mad at him for betraying one of the few friends he has and asks why he wants to quit. Will goes from wanting to tell Phil about the bribe to saying "I'd rather not say" so Phil wouldn't know his friend was a sleazy businessman. Plain and simple he'd rather have Uncle Phil be mad at him than have Uncle Phil lose one of his close friends.
And when it comes out anyway, Philip, despite great personal pain, stands up for his nephew to his friend and orders him to take his bribe and get out of the house. Will tries to cheer him up by putting on "Ain't Too Proud to Beg" and goading him into dancing around the living room (as Philip had been doing that with said friend at the beginning of the episode). All things considered, Will wants his uncle to be happy.
A lot of the interaction between Will and Carlton in "Blood is Thicker Than Mud," shows just how close they've gotten over the years. The pair are trying to get into an all-black fraternity and are putting up with typical hazing as pledges. The frat's head takes an instant disliking to Carlton for "not being black enough" and makes his hazing much harder than all other recruits, with the intention of never letting him in. When Will sees Carlton put up with all of it without complaining he starts by saying whether they get in or not he's proud of him (though he does get comically annoyed when Carlton tries to hug him afterward). Later when the frat leader tells Carlton just what he thinks of him, Will is about to rush to his defense, only for Carlton to stop him and say, in an understanding and appreciative voice, "I got this." After Carlton storms out, Will immediately follows his example, even quoting one of his cousin's corny jokes as he does so. It just displays the mutual love and understanding the pair have formed for each other by this point.
"'Twas the Night Before Christening" has Vivian ask Geoffrey, on Christmas, if he'll be Nicky's godfather. His face positively lights up.
Vivian: Geoffrey. Nobody loves Nicky more than you do... Would you do us the honor of being Nicky's godfather?
Geoffrey: Oh, Madam, I don't know what to say! This is the best Christmas gift I could ever get!
And then later, as Will walks in, Geoffrey proudly announces, toothy smile and all, "Master William, I'm Nicky's godfather!"
When the bickering Will and Lisa go to pre-marital counseling, the counselor gives them foam bats to work out their aggression. For that day's session, they are joined by George & Louise Jefferson, (at this point, it becomes obvious the episode is intended as an Homage to the "foam bat" episode from the previous series). Despite all their previous arguing, Will and Lisa are instantly ticked off when George and Louise make insulting comments about their respective partners and engage in an all-out brawl. By the episode's end, they realize that they have what it take to make a marriage work if they can stick together despite previous animosity.
In the Season 5 opener, Will gets Ashley a career in music. Phill and Vivian are stunned, and are not happy. When Ashley gets nervous however, Will and Carlton both dance to the song to give her confidence and Ashley very rapidly does a stellar performance. When the song is over, Will embraces Ashley and she gets a standing ovation.
A very underrated moment was in Season 1 when Will gets a new girlfriend who's a lonely intellectual in college. When Will learns that his relationship with her is damaging her grades and could get her kicked out of school, Will, under Aunt Viv's advice, tells her they need to send some time apart, which upsets her. Back at the dorm room, Aunt Viv, who is the girl's professor, tells her that she told Will to do that. The two then have a heart to heart conversation discovering they both had similar upbringings and Aunt Viv tells her that she needs to understand that even if she doesn't fit in and she's the last hope for her family, she does deserve to be where she is and she needs to believe that otherwise nothing anyone tells her will help. She then realizes it's better for Will and her to spend less time together.
In "Courting Disaster" Will is coaxed into joining the basketball team. In the first game, Will singlehandedly annihilates the opposing team and Uncle Phil couldn't be prouder of him and it starts bringing them closer together. This was probably the earliest true bonding moment between them.
Carlton feels slighted by this because Phil never came to the basketball games until now. At the end of the episode, Phil says he didn't mean to make Carlton feel unimportant, but he adds that he always makes time for his other activities and that Will really needed the extra attention.
"His mother is 3,000 miles away. He needs a cheering section as much as you do, maybe more."
In "Vying for Attention," Will feels slighted over his mom's new relationship and potentially starting a new family that doesn't include him. After grousing for a while, he runs off to a pool hall just to get away from it all. Carlton tracks him down to talk some sense into him.
Carlton: Will, I just want you to know if your mom abandons you and gets married, you'll always have me because, well, you're like the brother I've always wanted.
Real Life Example: After James Avery (Uncle Phil) passed away in 2013, his former co-stars paid tribute to him:
Janet Hubert (the first Aunt Vivian),
"RIP James, all the world is a stage, and we are all merely players in this production called LIFE."
One time Will begins to fear that he won't be able to get his life together, Uncle Phil chimes in his opinion about Will, admitting while Will does give him the most grief out of all the kids under his roof, he also said that he is also the one that he never worries about.