Klal Yisroel has the custom of staying up Shavuos night learning Torah. Many sources support this custom, the earliest of which is the Zohar, Parshas Emor (97b).
Magen Avraham (494) provides a reason for the custom based on the Midrash in Shir Hashirim Rabbah (1:12:2). The Jews overslept on the day they were to receive the Torah, and Hashem had to awaken them. To rectify this mistake, we stay awake all night yearly on Shavuos.
In Maayan Beis Hashoeivah (Shemos 19:17), Rav Shimon Schwab questions how the Jews could oversleep on the day they received the Torah. He explains that they believed Matan Torah would be a prophecy experienced while asleep, which was accurate for all Prophets except Moshe. They did not realize that the Torah's giving was even more significant than prophecy, requiring them to be awake.
Shiurei Halacha (Felder, 14:5) rules that even if one believes he will learn better over the rest of Yom Tov if he sleeps Shavuos night, he should still stay up and learn because following the custom is essential.
Another reason he gives is that just as on Rosh Hashanah we have Simanim (e.g., an apple in honey), which help us throughout the year, on Shavuos, which is the Day of Judgement for Torah (Shelah, Shavuos: ד"ה חייב אדם לשמוח), we have a siman of our love for Torah, which also helps us throughout the year.
He further explains that such a person who wants to go to sleep fulfills the custom to the highest degree, as he shows his love with the Torah even when it goes against his calculations. Thereby rectifying the mistake the Jews made by sleeping, which shows a lack of love.