The clock in the Swan counted down 108 minutes before the Numbers had to be entered into the computer. (Note: the alarm sounded at the four minute countdown mark, and the Numbers could be input any time after this). The clock reset itself to this number after the correct numbers had been input. If the counter reached zero, a set of hieroglyphs appeared in the counter instead. ("Adrift") ("Orientation")
108 x 5 = 540. 540 was the number of days until "your replacement" would arrive at the Hatch, according to the orientation film. ("Orientation")
Log printout from episode "?" which increments by 108 units in base 60.
108 was part of the video reel #23108-42 that Kelvin showed to Sayid. ("One of Them")
# on the log printout in the Pearl displays numbers that increment by 1:48 in base 60 (which we use for counting time). If we convert 1:48 from base 60 to decimal, we arrive at 108, which makes sense given that this is the frequency with which the code is entered. ("?")
More specifically, one of the Buddhist readings of the number 108 is as the quantity of Klesas (mental defilements) according to the Tentai version of the Abhidharma Abhidharma (one of the main Buddhist doctrinary texts). 
A typical Japanese interpretation for the meaning of the number 108, used by both Nichiren and Pure Land schools, is given under "Shoshu Buddhist" (Shoshu is a controversial Nichiren school of Buddhist origins).
Followers use 108 beads in their malas. They implement the following formula:
3 possibilities of sentiment [like, dislike, indifference]
Other outside occurrences
Mathematically 108 is associated with numerical powers. 1^1 * 2^2 * 3^3 = 1 * 4 * 27 = 108. Some theorize that this phenomenon was one of the reasons behind the religious significance of the number 108 since the ancient Hindu culture was among the first to derive such mathematical concepts as multiplication and powers.
The spherical angle between Los Angeles and Sydney is 108 degrees plus some decimal run over.
108 MHz is the highest band for FM radio broadcasts.
To help in preparing the instrumentation for the Trinity atomic bomb test the "100 Ton Test" was fired on 7 May 1945. This test detonated 108 tons of TNT stacked on a wooden platform 800 yards from Trinity ground zero.
History & culture
108 minutes is the time it took Juri Alexejewitsch Gagarin to circle around the earth on his first spaceflight.
On New Years in Japan the church ring a bell 108 times to rid the 108 evils in the body.
In Hungarian historic tradition, recorded in Simon Kézai's Chronicron Pictum which was written in the XIV. century, the Hungarian and Hunnic nations are both consisted of 108 genus or stem.
Stonehenge is 108 feet in diameter.
There are 108 stitches on a regulation baseball, such as the ones used by the Boston Red Sox.
In the martial art Wing Chun, each of the 3 forms, and the wooden dummy training traditionally consist of 108 movements.
Misty May and Kerry Walsh, the 2008 Olympic Gold medalists in women's beach volleyball have a streak of 108 wins.
The New York Mets won 108 games during their 1986 season when they won the World Series.
In the J.J. Abrams-produced television show Fringe, character Morgan Steig was passenger #108 on Flight 627.
In Fyodor Dostoevsky's short story "Notes From the Underground" the narrator muses that science will one day teach man that he possesses neither will nor uncontrollable urges and is nothing more than a piano key or organ stop operating by laws of nature, and that if discovered, these laws could be used to compute human actions mathematically like tables of logarithms up to 108 - 000.
In Homer's "The Odyssey," Odysseus is forced to fight off 108 suitors when he returns to his wife Penelope.
The Chinese classic Shui Hu Zhuan there are 108 Stars of Destiny, heroes who band together for the cause of justice.