The Whedon-verse was never really big on parenting. Buffy's parents were divorced -- and the original plan for the series was for them to never be seen at all. Willow's parents were rarely mentioned and even more rarely seen. Xander's parents only served to help break up his wedding. Giles's parents were mentioned once or twice, but never seen. Angel and Spike killed their parents. Tara's mom was dead and her dad was a jerk who only showed up once. Cordelia's parents committed tax fraud which forced her to forgo college. Even extending to Angel, the only positive parents on the show were Fred's. Excepting flashbacks, I don't think we ever saw parents at all on "Firefly" or "Dollhouse" (though we did get the episode where Jayne got the knit hat from his mom, so there's at least one mother-son relationship in "Firefly" that doesn't suck).
But then there's Joyce Summers. Buffy's mom -- and later Dawn's artificial memory mom -- is the one parent who gets to shine throughout the series, even beyond her death in Season 5. She essentially serves as the mother for all of the Whedon-verse.
Joyce, played by Kristine Sutherland, was the one character who was grounded in reality at the beginning of the series. She didn't know of Buffy's life as a slayer, and remained oblivious to it for two seasons while trying to make a better life for Buffy. She gets to balance caring with comedy, particularly in her spell-induced cougar moment with Xander in Season 2's "Bewitched, Bothered and Bewildered". At the end of Season 2, she finds out Buffy is The Slayer and blows up at her about all the lies throughout the years, but in a motherly fashion. She just doesn't want Buffy to walk away again, and wants her to sit down and talk about everything, but Buffy's gotta go save the world. The thing is, even though Joyce tells her "if you walk out of this house, don't even think about coming back", Joyce fully expects Buffy to come back, and is crushed at the end of the episode when she doesn't.
Of course, Buffy does come back at the beginning of Season 3, and their reunion is one of the most touching scenes in the entire run of the series. The relationship dynamic between Buffy and Joyce was changed after Joyce knew Buffy was the slayer, but even knowing her daughter was a super-powered world saver didn't stop Joyce's maternal instinct. She still just wanted to keep Buffy safe, taking it to extremes in "Gingerbread", when she started "Mothers Opposed to the Occult" (or M.O.O.).
Of course, Joyce wasn't always there. With Dawn's appearance in Season 5 came the emergence of Joyce's impending mortality in the form of a brain tumor. While there was never a definitive link made between the memories created to explain Dawn and Joyce's tumor, the timing seems more than coincidental. Joyce does her best to remain motherly in the face of her fading health. Don't forget, the first moment we meet Dawn comes along with Joyce telling Buffy, "if you're going out, why don't you take your sister?" It's such a "mom" thing to say.
Joyce's death at the end of "I Was Made to Love You" and the aftermath in "The Body" was probably one of the more emotional moments in the entire run of the series. I love that facing another apocalypse in "The Gift", in her moment of despair, Buffy said "I just wish... I just wish my mom was here."
Joyce made four more appearances after her death, but two were in flashback form. Her two major appearances post-death came in Season 6's "Normal Again" and Season 7's "Conversations With Dead People". Her scenes with Buffy, particularly her final goodbye, in "Normal Again" were just heartbreaking, and provided a nice bookend to "The Body", where it was Buffy having to say goodbye to Joyce, not the other way around.
Joyce appeared in 58 episodes in the 7-season run of "Buffy the Vampire Slayer", but if you're looking for some solid Joyce episodes to watch on this Mother's Day, here's what I would go with (leaving "The Body" out, because as amazing as it is, it's depressing as all hell):
"School Hard" - Season 2, Episode 3
Joyce's famous axe-waving "get away from my daughter" confrontation with Spike
"Ted" - Season 2, Episode 11
There's more than meets the eye to Joyce's new boyfriend, played by the late John Ritter.
"Becoming, Part 2" - Season 2, Episode 22
Joyce finds out Buffy is a slayer, and doesn't handle it well
"Dead Man's Party" - Season 3, Episode 2
Joyce tries to throw Buffy a "Welcome Back to Sunnydale" party. Zombies crash.
"Band Candy" - Season 3, Episode 6
Magical band candy turns Sunnydale's adults into teenagers (not physically, just in spirit), and Joyce and Giles make the best of it.
"Gingerbread" - Season 3, Episode 11
One word: M.O.O.
"Restless" - Season 4, Episode 22
Totally worth it for the Joyce-Xander dream sequence