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. ("?")
As it is now clear that the show has a recurring theme of religion, specifically Eastern religion (DHARMA, namaste), it is important to note that the number 108 has great significance attached in that realm. Note that the religious significance of 108 to many Eastern ideological beliefs also has great impact on their popular culture, as seen in the following "Occurrences outside the show" section.
There are 108 beads on a mala, used by Buddhists and Hindus for chanting.
More specifically, one of the Buddhist readings of the number 108 is as the quantity of Klesas (mental defilements) according to the Tientai version of the 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) in :
Followers use 108 beads in their malas. They implement the following formula:
3 possibilities of sentiment [like, dislike, indifference]
6^2 + 6^2 + 6^2 = 108. In common Christian Eschatology, 666 is the Number of the Beast. (This is currently being disputed)
Outside the show and real life 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 signicance of the number 108 since the ancient Hindu culture was among the first to derive such mathematical concepts as multiplication and powers.
In the J.J. Abrams-produced television show Fringe, character Morgan Steig was passenger #108 on Flight 627.
On New Years in Japan the church ring a bell 108 times to rid the 108 evils in the body.
108 minutes is the time it took Juri Alexejewitsch Gagarin to circle around the earth on his first spaceflight.
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.
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.
It took 108 years to end the Spanish-American War tax. In 2006, the Treasury Dept. ended a 1898 tax to fund the war.
108 = 0108 Hebrew Strong's number = mist, vapor of the ground whence clouds are formed, so called from surrounding and covering the earth like a veil. This derivation is confirmed by the Arabic root 'med', which is whatever guards and strengthens anything, defense. Also means atmosphere.
1-0-8 is the emergency telephone number in India (such as 9-1-1 is in the USA). A common saying in India is "Dial 108 and save a life".
The Chinese classic Shui Hu Zhuan there are 108 Stars of Destiny, heroes who band together for the cause of justice.
In the martial art Wing Chun, each of the 3 forms, and the wooden dummy training traditionally consist of 108 movements.
There are 108 stitches on a regulation baseball, such as the ones used by the Boston Red Sox.
On the Lost original television soundtrack the track "Me and my big mouth" is exactly one minute and eight seconds (1:08) long
The wave swimming pool at the Mandalay Bay hotel in Las Vegas cycles 1 wave every 108 seconds.
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.
108 is the ten code for officer down or officer in danger.
"National Geographic Magazine (March 2008) cites a repetitive Buddhist ritual in Bhutan involving 108 kernels of corn: "Each time the gray haired woman named Tum Tum prostrates herself [before a sacred pillar of stone], she slides one of the 108 kernels (a sacred number) across the floor. In three months she as moved the kernels 95,000 times - 1000 prostrations a day - and will continue until she reaches 100,000."
The spherical angle between Los Angeles and Sydney is 108 degrees plus some decimal run over. 
The exterior angles between the points of a pentagram, and the interior angles of a pentagon are 108 degrees.
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.
Stonehenge is 108 feet in diameter.
In Mac OSX 10.6 (Snow Leopard)'s "Wake on Demand" feature, roughly every 108 minutes or so, it's normal behavior for the computer in sleep mode to awaken briefly for maintenance, just enough to repair and resolve its current network state, and then to immediately return to sleep.
Episode 5 of Season 6, "Lighthouse," was the 108th episode of the series.
There are 108 pressure points in a human's body.
"The Walrus and the Carpenter", a poem written by Lewis Carroll is composed of 108 lines.
A binaural beat of 108hz is said to correspond to a state of consciousness called "Total Knowing."
The chronological beginning of the movie PULP FICTION takes place 1 hour and 8 minutes (1:08) into PULP FICTION.