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.
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 anyway 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 wager 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.
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 could 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."
Phil and Vivian once appeared on an episode of Soul Train when they were younger. The scramble was supposed to read "James Brown". Phil made it read: "Vivian, I love you and I always will. Marry Me?"