Perhaps you may already know this, and yet  to refresh your knowledge  I  give below the facts gathered about the greatness of the sacred number 108, which governs our life  as  found and established by our wise ancestors:When you read the  brief data given below you will  wonder how and
WHY   “108” IS   SACRED NUMBER ???..    
In one minute, we breathe in approximately 15 times, in 1 hour 900 times, and in 12 hours 10800 times, and in a day 10800 * 2 times.
A day consists of 24 hours, and if we set aside half the day for our day to day routines, then one can spend 12 hours for recitation of one's idol. Therefore, the maximum number of times that one can recite "mantra", or perform "Jap" are 10800. If one wants to obtain 100% benefit of its jap, then performing jap 108 times will give you the benefit of 100%.
 
That's why in a "Mala", there are 108 beads. It is written in Vedas, that 1 Jap corresponds to 1 mala (which has 108 beads), therefore performing jap of 108 malas will result in 100% benefit.

Astronomically, there are 27 constellations in our galaxy, and each one them has 4 directions, and 27 * 4 = 108, In other words the number 108 covers the whole galaxy. 
 
According to Indian scriptures, letter 9 corresponds to Lord Brahma (the creator of universe). Mathematically, the interesting property of 9 is
9 x 1 = 9
9 x 2 = 18 (8+1 = 9)
9 * 3 = 27 (7+2 = 9)
9 * 12 = 108 (1+0+8 = 9)

 
In Hindu religion, number 9 is very important. Keeping the importance of number 9, Rishi Vyas has created 9 Puranas, 108 Maha Puranas (Upnishads).
Mahabharatham  has 18 chapters, Geeta has 18 chapters, Bhagavatham  has 108000 Shloks (verses).

Indian Vedas, treat the Sun as God, and Sun has 12 signs (Zodiac signs). In Yajurved, Sun is related with Lord Brahma (the number 9), remember - 12 * 9 = 108; therefore for Gods Prayer, the number 108 is very sacred.
 
According to Indian mythology, there are 4 Yugas
Satyug - consists of                   172800
0 years (1+7+2+8 = 18 = (1+8 = 9)
TretaYug consists of                 1296000 years (1+2+9+6 = 18 = (1+8 = 9)
DwaparYug consists of             864000 years   (8+4+6)    = 18 = (1+8 = 9)
Kaliyug consists of                    432000 years   (4+3+2)     = 9 
 
Harshad number: 108 is a Harshad number, which is an integer divisible by the sum of its digits (Harshad is from Sanskrit, and means "great joy")

Desires: There are said to be 108 earthly desires in mortals.

Lies:      There are said to be 108 lies that humans tell.

Delusions: There are said to be 108 human delusions or forms of ignorance.

Heart Chakra: The chakras are the intersections of energy lines, and there are said to be a total of 108 energy lines converging to form the heart chakra. One of them, sushumna leads to the crown chakra, and is said to be the path to Self-realization.

Sanskrit alphabet: There are 54 letters in the Sanskrit alphabet. Each has masculine and feminine, shiva and shakti. 54 times 2 is 108.

Pranayama: If one is able to be so calm in meditation as to have only 108 breaths in a day, enlightenment will come.

Upanishads: Some say there are 108 Upanishads, texts of the wisdom of the ancient sages.

Sri Yantra: On the Sri Yantra there are marmas where three lines intersect, and there are 54 such intersections. Each intersections has masculine and feminine, shiva and shakti qualities. 54 times 2 equals 108. Thus, there are 108 points that define the Sri Yantra as well as the human body.  The angle formed by two adjacent lines in a pentagon equals 108 degrees.

Pentagon: The angle formed by two adjacent lines in a pentagon equals 108 degrees.
Marmas:
 Marmas or marmasthanas are like energy intersections called chakras, except have fewer energy lines converging to form them. There are said to be 108 marmas in the subtle body.
Time: Some say there are 108 feelings, with 36 related to the past, 36 related to the present, and 36 related to the future.

8 extra beads: In doing a practice of counting the number of repetitions of the mala, 100 are counted as completed. The remaining are said to cover errors or omissions. The 8 are also said to be an offering to God and Guru.

Chemistry: Interestingly, there are about 115 elements known on the periodic table of the elements. Most of those, around or higher than the number 100 only exist in the laboratory, and some for only thousandths of a second. The number that naturally exist on Earth is around 100.

Astrology: There are 12 constellations, and 9 arc segments called namshas or chandrakalas. 9 times 12 equals 108. Chandra is moon, and kalas are the divisions within a whole.

River Ganga: The sacred River Ganga spans a longitude of 12 degrees (79 to 91), and a latitude of 9 degrees (22 to 31). 12 times 9 equals 108.

Planets and Houses: In astrology, there are 12 houses and 9 planets. 12 times 9 equals 108.

Goddess names: There are said to be 108 Indian goddess names.

Gopis of Krishna: In the Krishna tradition, there were said to be 108 gopis of Krishna .

1, 0, and 8: Some say that 1 stands for God or higher Truth, 0 stands for emptiness or completeness in spiritual practice, and 8 stands for infinity or eternity.

Sun and Earth: The diameter of the Sun is 108 times the diameter of the Earth. The distance from the Sun to the Earth is 108 times the diameter of the Sun.

Moon and Earth: The average distance of the Moon from the Earth is 108 times the diameter of the Moon.

Silver and the moon: In astrology, the metal silver is said to represent the moon. The atomic weight of silver is ?108.

Numerical scale: The 1 of 108, and the 8 of 108, when added together equals 9, which is the number of the numerical scale, i.e. 1, 2, 3 ... 10, etc., where 0 is not a number.

Meditations: Some say there are 108 styles of meditation.

Breath: Tantra estimates the average number of breaths per day at 21,600, of which 10,800 are solar energy, and 10,800 are lunar energy. Multiplying 108 by 100 is 10,800. Multiplying 2 x 10,800 equals 21,600.

Paths to God: Some suggest that there are 108 paths to God.

Smaller divisions: The number 108 is divided, such as in half, third, quarter, or twelfth, so that some malas have 54, 36, 27, or 9 beads.

Hinduism: 108 is said to refer to the number of Hindu deities. Some say that each of the deities has 108 names.

Islam: The number 108 is used in Islam to refer to God.

Jain: In the Jain religion, 108 are the combined virtues of five categories of holy ones, including 12, 8, 36, 25, and 27 virtues respectively.

Sikh: The Sikh tradition has a mala of 108 knots tied in a string of wool, rather than beads.

Buddhism: Some Buddhists carve 108 small Buddhas on a walnut for good luck. Some ring a bell 108 times to celebrate a new year. There are said to be 108 virtues to cultivate and 108 defilements to avoid.

Chinese: The Chinese Buddhists and Taoists use a 108 bead mala, which is called su-chu, and has three dividing beads, so the mala is divided into three parts of 36 each. Chinese astrology says that there are 108 sacred stars.

Stages of the soul: Said that Atman, the human soul or center goes through 108 stages on the journey.

Meru: This is a larger bead, not part of the 108. It is not tied in the sequence of the other beads. It is the quiding bead, the one that marks the beginning and end of the mala.

Dance: There are 108 forms of dance in the Indian traditions.

Praiseworthy souls: There are 108 qualities of praiseworthy soul
First man in space:
 The first manned space flight lasted 108 minutes, and was on April 12, 1961 by Yuri Gagarin, a Soviet cosmonaut
The ancient Indians were excellent mathematicians and 108  is the product of a precise mathematical operation (e.g. 1 power 1 x 2 power 2 x 3 power 3)  ie,   1 to 1st power=1; 2 to 2nd power=4 (2x2); 3 to 3rd power=27 (3x3x3). 1x4x27=108
Heart Chakra: The chakras are the intersections of energy lines, and there are said to be a total of 108 energy lines converging to form the heart chakra. One of them, sushumna leads to the crown chakra, and is said to be the path to Self-realization.
Dance: There are 108 forms of dance in the Indian traditions.
Pythagoran:   9 is the limit of all numbers, all others existing and coming from the same. ie: 0 to 9 is all one needs to make up an infinite amount of numbers.
SHOSHU BUDDHIST
Followers use 108 beads in their malas. They implement the following formula:
6 x 3 x 2 x3 = 108
6 senses [sight, sound, smell, taste, touch, thought]
3 aspects of time [past, present, future]
2 condition of heart [pure or impure]
3 possibilties of sentiment [like, dislike, indifference]
BUDDHA’S FOOTPRINT
All Buddhists accept the Buddha Footprint with its 108 Auspicious Illustrations. These areas are considered to have been marked on the Buddha’s left foot when his body was discovered.
BUDDHISM
108 beads on the Hindu maalaa {rosary}
108 Arhats or Holy Ones
HINDUISM
108 Gopis {consorts} of Lord Krishna
108 Holy places for Vaishnavas
108 beads on the Japa maalaa {rosary}
108 Upanishads
108 Divyadesas  - Divine or Sacred Tirtha throughout India and Nepal
108 sacred water taps in Muktinath - Nepal
TANTRA SHASTRA
108 Pitha {Sacred Places}
The story goes that Lord Shiva was in deep and incessant meditation. His asceticism was creating great heat in the universe. All existence was in peril and Lord Brahma was deeply concerned. Lord Brahma asked the Mother of the Universe, Maa Shakti, to use Her strength and wile to seduce Lord Shiva. Maa Shakti agreed and was born as Sati, daughter of Shri Daksha. Lord Shiva was so entranced by Sati’s asceticism and extraordinary beauty that he took human form and they were married. Years later, at a feast, Sati’s father insulted Lord Shiva. Sati was so humiliated that she began a deep meditation which led to her immolation. Lord Shiva was completely heart broken. He reached into the sacrificial fire and pulled out as much of His beloved’s body as he could grab. As He ascended to heaven, bits of Sati’s body fell to earth. 108 bits to be precise! In time, these places were acknowledged and worshipped.
SANATANA DHARMA
In a book by Khurana, the explanation closely mirrors the original Vedic justifications:
A circle has 360 degrees, which when multiplied by 60 gives us 21,600 minutes in a circle. 60 comes from the 60 'ghatis' which Sanatana Dharmiks believe in. One ghati is equal to 24 minutes and 60 ghatis come to 24 hours.
One ghati is divided into 60 parts or 'palas'.
So the 60 ghatis multiplied by 60 palasa comes to 3,600.
This is further multiplied by 60 (becase a pala contains 60 vipalas) which gives us 21,600.
Half of this is for the day, and the other half for the night. So, 21,600
divided by 2 gives us 10,800. For practical purposes, we use 108. Using the
number 108 helps us coordinate the rhythm of time and space & we remain in harmony with the spiritual powers of nature.