Why do we worship the Shiva Linga?

shlokam: Divine, Out of the symbol (li~Ngam) that arose out of the quarrel of prime-ness (between braHma and viShNu), Matted hair crested, Keeping the hand on the hip, with the other hands holding deer and protection sign, in the right holding axe, having the braHma and viShnu (who sought) the Transcending feet and crown, as the swan above and boar below, that li~Ngodbhava I meditate. 

purANa of the deity li~Ngodbhavar: The Lord appearing from the symbol. (The principle behind linga worship) 

Once before the creation started, a quarrel broke between braHma and viShNu as to who is great. Brahma claimed he is as he is the creator of the whole world. viShNu rejected the claim saying the creation would not be useful without his sustenance of the world. The war of words between these two great divines worsened. At that point of time to make them realize the truth there appeared a pillar of fire. It was huge that both of them were astonished to see that. Now as a solution to their debate they wanted to decide who is the greatest by reaching the tip of that pillar. braHma took the form of a haMsa (swan) and went up to reach the top of that pillar, viShNu took the form of a wild pig and went down to reach the bottom of that pillar and it was agreed that whoever sees the either tip would be the greatest. 

That pillar was not any ordinary column of fire, it was the Supreme Itself, the One that is beyond form, color and qualities ! Who knows the start and end of that Supreme !! The two who set out on their strength to explore the endings of It went on and on only to become more and more tired and it was hopeless to find the end of It. viShNu returned realizing that it should be the parashiva which is beyond the limits that can be measured by knowledge, Which has come out of Its Grace to bless them and make them realize the Truth easily. He accepted his failure. braHmA on the other hand, though realizing it is impossible to see the top of the fire column, returned lying that he saw the tip. The lie stood exposed and hence he is not worshipped. Now both of them realizing the greatness of the Supreme worshipped the Lord shiva, the Gracious one, with lots of devotion and sincerity. The Lord out of the grace to bless all the pashus (souls) with a way they could easily understand and worship the Supreme, Which is unexplainable, unexplorable, appeared as a li~Ngam which is a vertical pillar resembling the flame. As it resembles the flame, It is neither a form nor a formless, but is just a symbol of the Supreme jyoti. The Lord later appeared in a form and blessed viShNu and braHma. This Lord is called li~Ngodbhavar. 

This form which came out of the formless Supreme out of Its grace to bless the sincere worship of braHma and viShNu and which is a from but represents the formlessness of the Supreme is considered very holy by the shaivites. The shiva li~Nga (meaning symbol of shiva) is the foremost of all the shaivite worships. As the ash would be closely associated with the fire, Holy Ash is associated with this Fire pillar Lord and sacred for the shaivites.