Why do we worship Lord Ganesha

Why is Lord Ganesha first worshiped before a puja?

@AksharRoop and @Tejesh Alimilli have already explained two mythological stories that tell us how Lord Ganesha became the 'Pratham Pujya' (the one to be worshiped first). Let me give you one more reason why Lord Ganesha is worshiped before I begin a task.

Yogic Belief:

From the yogic perspective, Shri Ganesha, the Eternal Child (from Adi Shakti), is the presiding deity for the Muladhara Chakra. He is the embodiment of innocence and he guards his mother Kundalini (Adi Shakti) and her instrument with great vigilance and uncompromising zeal.

According to Ganapati Upanishad :

Lord Ganesha is eternal and appeared before the creation of nature (Prakriti) and consciousness (Purusha). which means that he appeared before the creation process.

From this page :

"Before humans were created, before the earth and the sky, long before the sun, the moon and the galaxies, I (Shri Ganesha) filled everything with holiness and innocence. Single-handedly, the Holy Spirit of Mother, Adi Shakti (Shri Ganesha) first to protect and protect her everywhere. My total devotion to her (Adi Shakti) and my exclusive alliance with her can remove any obstacle. In your body I am innocence, wisdom and spontaneity. I am the holiness of marriage union and the blessing of holy children. When Kundalini awakens my presence in you you will regain your lost innocence. It overcomes all of its enemies outside as well as those within you. I am the eternal child and the sparkle of my innocence radiates from the universe in a constant flow of bliss. "

Shri Ganesha was created by the Adi Shakti, the primal power of God, the Almighty, without the cause of the male-female principle. He was born of the primordial mother and is with her all the time and in the Muladhara Chakra in people. He is the embodiment of innocence, purity and chastity in creation.

This could be one of the reasons people worship Lord Ganesha before starting the marriage process and on marriage invitation cards. As well as keeping idols of Lord Ganesha in their cars, doorways, etc.

Ganapati Atharvashirsha says: Shri Ganesha lives always in the "MULADHARA" chakra of our body and has the power of the Trinity (creative maintenance and destructive powers). He is Trigunatmak by having 3 'GUNAS' (Satva: Pure, Rajas: Activating & Tamas: Dull).

Tvam Guna Traya Atitaha
Tvam Deha Treya Atitaha
Tvam Kala Treya Atitaha
Tvam Avastreya Atitaha
Tvam Muladhar Stiti Yosi Nityam
Tvam Shakti Treya Atmakaha
Tvam Yogino Dhayayanti Nityam
Tvam Bramhastvan, Vishnustvam, Rudrastvam, Indrastvam Agnistvam, Vayustvam, Suryastvam, Chndramastvam, Bramha Bhur Bhuva Svorom || 6 ||
Importance:
You (Shri Ganesha) are beyond the 3 'GUNAS' (Satva: Pure, Rajas: Activating & Tamas: Dull)
You are beyond the 3 bodies; (Gross, subtle & casual)
You are beyond past, present and future (3 time states)
You are beyond 3 states of being; (Awake, dream & deep sleep)
You always live in the "MULADHARA" chakra
You are the trinity of power; (Creative maintenance and destructive powers)
Sages always meditate on you
You are the creator. Preserver, Destroyer, The Lord of the 3 Worlds, Fire, Air, Sun, Moon, You are all inclusive and all pervasive || 6 ||

Ramdas Swami Manache Shlok 1 : Ramdas Swami also explains that Shri Ganesha remains in the Muladhar Chakra of his body, where Kundalini Shakti sleeps here, waiting to be aroused with the blessings of Lord Ganesha and to come to Brahman (the Absolute).

Ganadhish Jo Ish Sarwa Gunancha
Mularambh Arambh to Nirgunacha
Namu Sharada Mul Chatwar Wacha
Gamu panth aanat ya raghawacha || 1 ||

That means: let's hunt the god Ganapati, who is the leader of all Gana (Ganadhish), who is the Lord of the various divine virtues (Uttam Gun), which is the starting element of non-physical existence (nirgun) . We pray to Lord Ganapati to succeed in our mission (to prepare for a life of improvement). We then pray Maa Saraswati, who is the pioneering energy of the universe for its operation in the form of four sound levels (Chatwar Wacha: Para, Pashyanti, Madhyma and Waikhari). With the prayer to Ganadhish and Sharada (after they have understood their forms: knowledge or energy). We seek their grace (aashirwad) to make the ideal life possible (as Lord Ram showed in his Avataar). We want to walk our lives on the path (panth) as Lord Ram (raghav) and endlessly (aanant) showed.

Everything we do must fall under one of two categories: material or spiritual. As we know, Lord Ganesha rules the 'Muladhara Chakra' of our body. 'Muladhara Chakra' is the interface between the material and the spiritual world. Lord Ganesha is said to control both worlds. He is the one who gives the material pleasures in this world, and He is the one who sets us free from the endless cycle of birth and death. Our material life as well as our spiritual journey begins with the 'Muladhara Chakra' which is controlled by Lord Ganesha.It is He who informs Kundalini when it is time to awaken and attain Nirgun Nirakar Swarup (Brahman).Therefore, in order to complete our life cycle without obstacles, we need the blessings of Lord Ganesha. Since he is the one who removes all obstacles from our life, we worship Lord Ganesha before starting any important work / assignment.

Keshav Srinivasan ♦

Note that the Ganapati Atharvashirsha Upanishad is generally not considered an authentic Upanishad. See my answer here: hinduism.stackexchange.com/a/3012/36