All of the participants of Buffy's birthday party, including anyone else who entered the house, being trapped inside the Summers residence by Dawn Summers' unwitting wish to Halfrek during her 21st.
Her birthday is listed as 10/24/1980 on her high-school registration 
In Nightmares her tombstone reads 1981 to 1997. Since this is Rupert Giles' nightmare, perhaps he doesn't know her actual year of birth? More likely it is just a continuity problem. 
In Doomed Buffy claims to be "Capricorn on the cusp of Aquarius", which implies her birthday is somewhere between January 17th and 23rd.
Behind the scenes
Whenever Buffy's birthday was celebrated on-screen, it was always during the twelfth or thirteenth episode of the season.