Lord Shiva has been worshipped in India for several thousands of years. At the same time, many in India will scoff at the idea of “worshipping” Shiva because Shiva represents our own true nature,  the one Absolute reality, no-thing and emptiness and so Shiva is something to be sought within and merged with. Yogis revere Shiva as the first yogi (Adi yogi) who passed down the yogic science to humanity.
Here are some beloved chants, mantras and songs of Lord Shiva. Each one is different in style and mesmerizingly wonderful in its own way.
1) Karpur Gauram
A soul-stirring rendition of this ancient Sanskrit shloka by guru Sadhguru Jaggi Vasudev.
2) Shiv Panchakshara Stotram
Composed by Adi Sahankaracharya (c.8th century CE), this strotam is well-known for expressing devotion to Shiva. This rendition by singer Shri Rameshbhai Oza is simply beautiful. The meaning of the lyrics is well explained here.
3) Shiva Shambho
A soulful version of this popular song by Shivaratri Café.
4) Nirvana Shakatam
Another composition of Adi Shankaracharya, this chant strikes a chord with every true seeker of Truth. This rendition is by Sounds of Isha. The meaning of the chant is explained here.
5) Om Namah Shivaya
Om Namah Shivaya is considered to be one of the most powerful chants offered to Lord Shiva. This ~13min version by the Art of Living which repeats the chant 108 times in a lovely melody. The number 108 holds a special significance in Hinduism as it expresses cosmological truths (1).
6) Shivoham
Shivoham means ‘I am Shiva’. This mantra has been used by yogis since times immorial, to remind themselves of their Absolute nature. This rendition by Bhanumathi Narasimhan of the Art of Living is incredibly peaceful.
7) Mahamrityunjaya Mantra
Also known as the Tryambakam mantra, this mantra is a verse from the Rig Veda (and also recurs in the Yajur Veda).(2) The mantra is associated with overcoming fear, healing and rejuvenation. It is also considered to bestow longevity and immortality as the term ‘Mahamrityunjaya’ translates as the ‘great conqueror of death’. In the highest sense, it is a plea for liberation (moksha).
This rendition by 21 Brahmins transports one right back to ancient Vedic times.
8) Shivashtakam
This piece by the venerable maestro Pandit Jasraj is one of his many renditions that are so divine and magical that they seem to belong to another world. It is as if it’s not the taal that holds up the song but the surrender and bhakti coursing through it.
(1) For an explanation of the significance of the number 108, see: Art, Cosmology and the Divine| Part II : General Equivalences by Subhash Kak
(2) Source: Wikipedia
See also: Shiva Panchakshara Stotram and  Seeking Shiva