When is the halacha like Bais Shammai and not Bais Hillel? Are there overarching principles that apply?
What are the cases? Is there a good reference that summarizes them?
This kind of questions are generally in masechet Eduyot.
Masechet Eduyot 1, 12 until the end of the perek, 5, several Mishnayot with Kule BS.
Shabbat 1, 4:
Succa 2, 7:
Tosfot in Succa 3a in name of Rav Amram Gaon listed 6 places, one of them is in the answer of Loevian, in the 8th chapter of berachot:
דאמר לך מני ב''ש היא ולא תזוז מינה כו'. בסדר רב עמרם פסק בששה מקומות הלכה כב''ש
חדא האי דסוכה צריכה שתהא מחזקת ראשו ורובו ושולחנו Succa Mishna 2, 7;
ואידך במנחות פרק התכלת (דף מ. ושם) גבי סדין בציצית ב''ש פוטרין וב''ה מחייבין In Mishnayot 4rd chapter of Menachot concerning tsitsit on a sadin;
עוד לשם כמה חוטין הוא נותן ב''ש אמרי ד' ובה''א ג' There, for number of wires in tsitsit;
עוד התם כמה תהא משולשלת בית שמאי אומרים ד' ובה''א ג' בכל הני עבדי כב'' There concerning triple loops in tsitsit;
ואידך במסכת ברכות פרק אלו דברים (דף נא:) בש''א מכבדין [את] הבית ואח''כ נוטלין לידים ואמרינן בגמ' בכוליה פירקין הלכה כב''ה בר מהך Several Halachot Seuda in 8th chapter of Berachot
עוד התם בסוף פירקא גבי מי שאכל ושתה ולא בירך דמייתי בגמרא עובדא דרבה בר בר חנה דאשכח יונה דדהבא וחד תלמיד דעבד כב''ש ואשכח ארנקי ואידך תלמיד דעבד כב''ה ואכליה אריה About changing place for Birkat Hamazon.
There are also cases in which Bet Hillel finally take Bet Shammai's opinion at the end of the first chapter of Eduyot. Eduyot The overarchic principle is that when nothing is said, Halacha as BH, Mishna said that the reason for the predominance of Bet Hillel is their humbleness, see Eruvin 13b(1), but decisions were reached by voting. There is also a list of cases in which BH is the stringent and BS the lenient in the fourth chapter of Eduyot, there are aslo lists of chachamim who agreed with BS for particular topics.
R'Abba stated in the name of Samuel: For three years there was a dispute between Beth Shammai and Beth Hillel, the former asserting, 'The halachah is in agreement with our views' and the latter contending, 'The halachah is in agreement with our views'. Then a bath kol issued announcing, '[The utterances of] both are the words of the living God, but the halachah is in agreement with the rulings of Beth Hillel'. Since, however, both are the words of the living God' what was it that entitled Beth Hillel to have the halachah fixed in agreement with their rulings? Because they were kindly and modest, they studied their own rulings and those of Beth Shammai, and were even so [humble] as to mention the actions of Beth Shammai before theirs, (as may be seen from what we have learnt: If a man had his head and the greater part of his body within the sukkah but his table in the house, Beth Shammai ruled [that the booth was] invalid but Beth Hillel ruled that it was valid. Said Beth Hillel to Beth Shammai, 'Did it not so happen that the elders of Beth Shammai and the elders of Beth Hillel went on a visit to R' Johanan B'Hahoranith and found him sitting with his head and greater part of his body within the sukkah while his table was in the house? ' Beth Shammai replied: From there proof [may be adduced for our view for] they indeed told him, 'If you have always acted in this manner you have never fulfilled the commandment of sukkah'.) This teaches you that him who humbles himself, the Holy One, blessed be He, raises up, and him who exalts himself, the Holy One, blessed be He, humbles; from him who seeks greatness, greatness flees, but him who flees from greatness, greatness follows; he who forces time is forced back by time but he who yields to time finds time standing at his side.
The Mishna in Chapter one, Mishna 4 of Tractate Shabbat says that they once took a head count and found there were more representatives of Beit Shamai than Beit Hillel and that day they decided 18 Halachot according to Beit Shammai.
Rabbeinu Ovadiya MiBartenura lists them all.
I don't know if that's all the places we rule like Beit Shammai, though.