Buffy's prophetic dreams gave several hints about Dawn long before her arrival. In 'Graduation Day, Part 2', season 3, dream Faith tells her 'little sis' is coming', and in 'Restless', season 4, dream Tara warns her 'Be back before Dawn'.
There have been several lines throughout the series have referred to Tuesday ('There's a demon trying to destroy the world and it's just another Tuesday night in Sunnydale' in Revelations and 'Dawn's in trouble. Must be Tuesday' in Once More With Feeling). These are references to the fact that, in the USA, Buffy is aired on a Tuesday.
In the final episode when Buffy, Xander, and Willow are wandering off talking about shopping, Giles turns round and says "The Earth is definitely doomed!" This is a little tribute to the end of the episode 'The Harvest' when Buffy, Xander and Willow wander off talking nonsense and Giles turns round and says a similar thing.
The 'Grrr Arrrg' monster at the end of each episode (ie. the mascot for Mutant Enemy Inc.) is something that alot of people watch through the credits to see. But if you watch at the end of 'Becoming', he walks past and says 'Boo hoo, I need a hug'...and at the end of 'Once More With Feeling' he sings his 'Grrr Arrrg'...and in the Episode 'Bargaining Pt. 1' Tara gives Giles a small monster as a goodbye present, 'Something to remind you of Sunnydale...' and then goes 'Grrr Arrrg'....Ain't little monster's grand. Also at the end of the Christmas episode where Angel tries to kill himself, the monster is wearing a santa hat, and, at the end of the graduation episode, the monster is wearing a mortar board.
Buffy's chums are regularly referred to as 'The Scooby Gang' which is funny, because Sarah Michelle Gellar actually went on to become an original Scooby as Daphne in Scooby-Doo, the movie.
Many elements of Xander's dream in 'Restless', season 4, were seen again in the season 6 episode 'Tabula Rasa'. In the dream, Spike wears a tweed suit and tells Xander he's in training to be a Watcher (Giles adds "Spike's like a son to me."), also mentioning 'A shark, but on land. A land shark'. In 'Tabula Rasa' Spike is under threat from a loan shark (literally a shark), disguises himself in a tweed suit and after a spell gone wrong believes he might be Giles' son.
Buffy and Willow were the only characters who appeared in every episode. Because it would have been difficult to incorporate a storyline for him, Xander is missing only from "Conversations With Dead People."
During Buffy's dream at the start of the episode Surprise, we see Willow sitting in the Bronze with a small monkey. Willow says, in French, "L'hippo a piqué ses pantalons" which translates as "The hippo has stolen his trousers." At the end of the episode What's My Line Part 2, when talking about Animal Crackers, Oz and Willow talk about the monkey being the only one to wear trousers, the hippo questioning why he hasn't got any, and the monkey being French.
In the episode 'The Replacement' Buffy asks what they're going to do with the 2 Xanders who then say 'Kill us both Spock'. This is a reference to an episode of Star Trek where Kirk ended up with an evil twin and Spock didn't know which one to kill, the real Kirk told Spock to kill them both so Spock killed the other one.