A memorable one would have to be the one when Justin is willing to give up his wizard powers for Alex, saying that if she doesn't have powers, then he doesn't want to have them either, because Alex is the one who makes him a better wizard. Then they hug longingly and smile at each other.
And now, the ending scene of Wizards Vs. Angels, where they share one of their famous (infamous?) hugs again.
At the end of the episode "Third Wheel", Alex declares Harper to be her sister, and they declare their love for one another.
"I'll always have my Harper." Which might also qualify as a Crowning Moment of Les Yay.
In "Alex's Logo," when all the other students are mocking Alex, Mr. Laritate takes the heat off her by deliberately making a fool of himself in front of the students so they will mock him instead.
The ending of "Moving On" once it's revealed what's happening. Justin's still feeling sad over losing Juliet and Harper has had enough of seeing him like this. Since he's not moving on, she asks Alex to cast a spell on her to make her impersonate Juliet for long enough to convince Justin to start loving again. After a series of mishaps, Harper tells Justin that while he might never find a girl like Juliet again, he will find a girl he'll like and just need to be open. Justin agrees, and kisses Harper on the cheek as thank you.
Then there's the credits scene. Justin has taken the advice to heart and is on a date with a girl flirting with him earlier in the episode. As they have a good time, the real Juliet, old and all, is seen hiding in the bushes, watching the couple with a smile.
Teresa & Jerry's marriage. He actually won the power in his family but when he fell in love with Teresa, he gave them up because he loved her so much and wizards can't marry non-wizards. Their relationship is actually extremely realistic towards actual marriages, despite being on a Played for Laughs comedy show.
When Max returned to his initial form, after he has been trapped into a little girl's body for quite long. He looks at the school's surroundings and mutters to himself it's good to be back....
Also, little before that, Max hugs each of his family members separately.
The Movie has lots and lots of these moments between them. Here are some:
Alex: Justin, what if we don't get the stone in time and we can't save everyone?
Justin: Don't worry about it. We will.
Alex: How do you know that?
Justin: Because it's you and I. How can we not?
Also, in the same scene:
Alex: You're a great wizard, Justin.
Justin: I just know a bunch of spells. How does that make me great?
Alex: That isn't why I think you're great.You're always there for me, no matter how many times I screw up...
Justin: That doesn't make me great. That just makes me a good brother.
Alex: You know I don't say it very often...but thank you.
Justin: You're welcome.
Justin loses his memory and Alex starts crying. Then she spills her feelings, proving that she's not quite the manipulativeHoudini we have all seen in the show:
Justin: Why would I help you?
Alex: ...Cause you're my brother... look, I'm sorry you didn't...
Justin: I'm your brother?
Alex: ...No, no... no, Justin... please, please, you can't leave me here, please remember... I'm Alex, I'm your little sister... I taunt you and I tease you and I make your life miserable, but you love me anyway... You're everything that I have ever wanted to be... I'm jealous of how, how smart you are and how kind and how nice... Please don't leave me here...
Justin: I'd never leave you. I don't know who you are... but... but I believe you. *They hug.*
When Max disappears, Theresa's scream is particularly heartbreaking. As is her later dialogue with Giselle.
Theresa: Look, I don't know what't going on. I'm not part of your world. I do know that I just got my heart ripped out by this boy that I didn't even know I knew, let alone loved. And his father, who may or may not be my husband. I wouldn't even mind if he was my husband. And these other two kids, these wonderful kids... Look it's a long story. But they need that stone, and I intend to get it.
Giselle: ...From what I could see, it didn't look like you and your daughter got along so well. There are a lot of moms who would like to be in your position.
Theresa: There isn't one!
And finally, when Alex wishes everything back to normal. The expression on her face when Theresa yells at her is heartwarming, and Alex hugs her. And when she realizes Justin and Max are back, runs to hug them, and then ends up arguing with Justin about the wizarding competition until Max goes "I'm right here," to which Alex responds "Yes you are, and I love you for that!" and glomps him.
In "Wizards Vs. Everything" when Juliet (who was revived and returned to her normal state somehow) re-unites with Justin at long last and they both hug.
Alex going back to Mr. Laritate to get a proper graduation.
In the Grand Finale, when the three Russo siblings took matters into their own hands and decided to run the sub shop themselves after Jerry decided to sell it. They were at first at each other's throats for having thought that they were disqualified from the wizard competition. Through a montage, they were shown working together and slowly softening up to one another, bringing their parents back as well. It brought tears to this troper's eyes, but they were Tears of Joy.
In the Alex V.S. Alex special, after enduring immense crap for the entire special and losing her powers and getting more crap by the Council and her father over her "responsibility" as the Family Wizard and about "changing", Alex tells it straight forward that she's tired of being told to change just because she's the Family Wizard, stating that it was only Harper that was the one who told her she was amazing as who she is, even saying she's happy to not have her powers as she has Harper. This actually makes everyone apologize to Alex and touched by her confession, the Council give her back her powers. Hot damn.
A Wizards of Waverly Place meet-and-greet was scheduled for a day when it was raining. In gratitude for the fans staying in line in the rain to meet them, Selena Gomez, Jennifer Stone and David DeLuise shot a short video where the three of them were soaked by fire hoses. Since the fans got soaked and cold, they could too.
At the 2009 D23 Expo, Selena told the story of a fan who came up to her, asking, "Alex? Is the magic real?" She asked him, "Do you believe it's real?" He was almost crying when he said, "Yes, I do believe it's real." She smiled and told him, "That's all that matters."
A most recent one is all six cast members coming together at David Hendrie's wedding. You can feel that despite going separate ways, they are still the Russo family we know and love through thick and thin. Jennifer Stone has two pics of the whole thing here and here.