R. Yerachmiel Zelcer published his Ner Le-Me’ah, a collection of 100 answers to the Beis Yosef’s question...

They divided the oil into eight parts and used one-eighth each night
After they filled the menorah each night, the bottle of oil was miraculously refilled
On each morning, they found the menorah refilled with oil
Not all the oil burned the first day so a little would remain on the second, because a blessing/miracle can only impact an existent item
One day of Chanukah celebrates the military victory
The first day commemorates the rededication of the Temple by the Hasmoneans
The eight days correspond to the eight days of circumcision, which the Greeks outlawed
The receptacles used as a menorah were broken and could not contain a full day’s amount of oil but still miraculously burned for a full day
The first day commemorates the dedication of the Second Temple when it was built – R. Yaakov Emden
Finding the bottle of pure oil was in itself a miracle
The Geonic work She’eiltos has a different version of the Talmudic passage (as it often does) which reads that they did not even have enough oil for one day
There was only enough oil for the first night but the menorah must be lit all day also
They were forbidden to extinguish the fire on the morning of the first day in order to conserve oil yet the oil continued burning through the eighth evening
The eighth day is celebrated out of doubt, as all holidays are observed outside of Israel
They planned on using multiple wicks dipped in the oil but the original wicks miraculously lasted all day
They lit in the courtyard rather than the inner chamber. The greater wind created a need for more oil
The month of Kislev was short that year but is now long (29 vs. 30 days). We still observe the holiday from 25 Kislev through 2 Teives even though it is now eight days rather than the original seven
On the first day, after they found the bottle with only enough oil for one day, it miraculously became enough for eight days
There was enough oil for lighting the menorah but not for relighting the western light in the morning, as it was each day
They thinned the wicks so they would only use 1/8th of the oil. The miracle was that the flame was as strong as if they used full wicks
The bottle only had enough for one light for one day but it lasted for all seven lights for eight days
They lit the menorah before dark on the evening of 24 Kislev, so the miracle also applied to the end of the first day
We are not allowed to make a replica of Temple utensils. We therefore celebrate for eight days so the menorah will have eight branches, rather than seven like the Temple menorah
Eight days like Sukkos
The miracle was not in the quantity of oil but the quality, that it burned eight times slower than normal, which also occurred on the first day