Who knows one hundred twenty?
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120 were the years of the following great leaders: (End of Sifrei)
Moshe rabbeinu (already mentioned by Gershon): 40 years by Paroah, 40 by Midyan, 40 as the leader of BN"Y
Hillel haZaken: At 40 y/o he ascended from Bavel, 40 years he served under Chachamim, 40 as leader of Israel
Rabbi Yochanan be Zakai: 40 years in business, 40 serving under chachamim, 40 as leader of Israel
Rabbi Akiva: At 40 he learned torah for 40 years, 40 years leading Israel
There are 120 sections in R' Shneur Zalman of Liadi's Tanya:
Moshe spent 120 days on Har Sinai.
40 for the first luchos
40 days praying for the b'nei Yisrael
40 days for the second luchos
Shimon the son of Yaakov Avinu lived 120 years.
Moshe Rabeinu lived 120 years.
Noach built a Teiva for 120 years.
The Knesset has 120 MKs.
A city must have 120 men to have a sanhedrin (Rambam Hil. Sanhedrin 1:10):
23 for the sanhedrin
69 backup judges (3 rows of 23)
10 "batlanim" for the beis hakenesses
2 court officials (chazanim)
2 baalei din
2 cancelling witnesses "zom'min"
2 cancelling witnesses of the cancelling witnesses "zom'mei zom'min"
2 tzedaka collectors
1 additional person to accompany the tzedaka collectors
1 expert doctor (to be an expert witness)
1 school rebbi
Kaddish D'Rabanan in Nusach Ashkanaz has 120 words (includes V'Arah, Tovim, B'Rachamov)
The Beis Hamikdash was 60 cubits long = 120 feet (Melachim1 6:1)
Chiram sent Shlomo HaMelech 120 talents of gold (Melachim1 9:14)
The Queen of Sheba gave Shlomo HaMelech 120 talents of gold (Melachim1 10:10)