Ajanma

"He is the king of the world, the Lord of tears, the great seer from whom the gods are born and into whom they merge in the end. May he, who first saw the birth of the universal Intellect, endow us with understanding."
~Shvetashvatara Upanishad

Shiva is Ajanma, the unborn God, who was, is and shall be even after eternity.

After a 100 years Brahma years, Brahmadev will die and a new Brahma will be born. After a 100 Vishnu years, Vishnu will die and a new Vishnu will be born. However, Shiva is eternal.

However, there are some stories on the birth of Rudra, a vedic-manisfestation of Shiva.

There are many stories in the Puranas about the origin of Rudra. According to the Vishnu Purana, at the beginning of this kalpa Brahma wanted a child and meditated for one. Presently, a child appeared on his lap and started crying. When asked by Brahma why he was crying, the child replied that it was because he did not have a name. Brahma then named him Rudra, meaning "howler". However the child cried seven more times and was given seven more names. Shiva therefore has eight forms: Rudra, Sharva, Bhava, Ugra, Bhima, Pashupati, Ishana, and Mahadeva, which, according to the Shiva Purana, correspond to the earth, water, fire, wind, sky, a yogi called Kshetragya, the sun, and the moon respectively.