How many Rudras have been actually born?

Question

We have been told that the Rudras were the incarnation of Lord Rudra (Shiva).

Who they actually were and how many were they ?

What were their duties ?

and will they come again in future?

Answer 1

The answer is there are infinite Rudras. In the SataRudriya section of YajurVeda (16th chapter) there is mention of various forms of Lord Rudra which are present in Heavens, in Earths, in Trees, in Antariksha, in heart of Gods etc.. etc..

Specially in the 11th Anuvaka various Rudra ganas are talked of which are identical to Rudra. Also in the 11th Anuvaka:

नमो रुद्रेभ्यो ये पृथिव्यां येऽन्तरिक्षे ये दिवि येषामन्नं वातो वर्षमिषवस्तेभ्यो दश प्राचीर्दश दक्षिणा दश प्रतीचीर्दशोदीचीर्दशोर्ध्वास्तेभ्यो नमस्तेनो मृडयन्तु ते यं द्विष्मो यश्च नो द्वेष्टि तं वो जम्भे दधामि ॥

We render obescience to those myriad manifestations of Rudra whose weapons are food, air and rain; who exists in earth sky and heaven. Prostrations to the east, to the south, to the east and to the north and upwards. Let them render us happy, whoever hates us and whosoever we hate consign in your wide open mouth.

The same thing is also confirmed by Grihya Sutras. For eg. Paraskara Grihya Sutra states:

12. A forest (through which he is wandering) he addresses: 'Adoration to Rudra who dwells in the forests. Make me arrive safely.'
    
    
13. A mountain (which he is going to cross) he addresses: 'Adoration to Rudra who dwells on the mountains. Make me arrive safely.'
    
    
14. A burial-ground he addresses: 'Adoration to Rudra who dwells among the Fathers. Make me arrive safely.'
    
    
15. A cow-stable he addresses: 'Adoration to Rudra who dwells among the dung-heaps. Make me arrive safely.'
    
    
16. And wheresoever else it be, let him always say, 'Adoration to Rudra.' For the Sruti says, 'Rudra is this universe.'
    

And also in the Mahabharata:

He was clad in a tiger-skin, had matted locks on his head, and bore the staff in one of his hands. He was armed, besides with his Pinaka and the thunderbolt. His teeth was sharp-pointed. He was decked with an excellent bracelet for the upper arm. His sacred thread was constituted by a snake. He wore an excellent garland of diversified colours on his bosom, that hung down to his toes. Verily, I beheld him like the exceedingly bright moon of an autumnal evening. Surrounded by diverse clans of spirits and ghosts, he looked like the autumnal Sun difficult of being gazed at for its dazzling brightness. Eleven hundred Rudras stood around that Deity of restrained soul and white deeds, then seated upon his bull. All of them were employed in hymning his praises. The Adityas, the Vasus, the Sadhyas, the Viswedevas, and the twin Aswins praised that Lord of the universe by uttering the hymns occurring in the scriptures.

And in the Kurma Purana in the chapter 'Creation by Rudra' Lord Rudra begins to create himself and there becomes billions and billions of his forms.

Thus there are uncountable, billions and billions forms of Rudra. However there are special groups of Rudras which have special tasks some of which I discuss in my answer here.

The famous groups are groups of Ekadash Rudras and groups of AshtaMurti Rudras;

Ekadash Rudras are:

They were Mrigavayadha, Sarpa, Niriti of great fame: Ajaikapat, Ahivradhna, and Pinaki, the oppressor of foes; Dahana and Iswara, and Kapali of great splendour; and Sthanu, and the illustrious **Bharga. These are called the eleven Rudras. [Adi Parva, Sambhava Parva chapter 66]

AshtaMurti Rudras are:

You are Rudra. You are Sarva. You are Pasupati. You are Ugra. You are Asani. You are Bhava. You are Mahadeva. You are Ishana. (Yajurveda Shatapatha Brahmana)

I discuss significance of them in my answer here.

Thus there are uncountable very large no. Of Rudras of which 11 Rudras and 8 Rudras are quite famous.

Answer 2

As per a standalone verse in the Liṅga Mahā-Purāṇa, Śiva created 28 crore Rudras.

Chapter 76 - Part I - Liṅga Purāṇa

सृष्ट्वा स्थितं हरिं वामे दक्षिणे चतुराननम् ।
अष्टाविंशतिरुद्राणां कोटिः सर्वांगसुप्रभम् ॥ ७६.९ ॥

पंचविंशतिकं साक्षात्पुरुषं हृदयात्तथा ।
प्रकृतिं वामतश्चैव बुद्धिं वै बुद्धिदेशतः ॥ ७६.१० ॥

9. & 10. The Lord who's stationed after manifesting Hari from his left side, and Brahmā from his right side. The Lord who created 28 crores of Rudras, and then the twenty-fifth principle Puruṣa, brilliant in all limbs from his heart; the Lord who created Prakṛti from his left, cosmic intellect from the regions of the intellect.

English Translation by Prof. J.L. Shastri

Answer 3

There are eleven Rudra-s. See their names in the translation from Gambhirananda:

BG 10.23 - Among the Rudras [Aja, Ekapada, Ahirbudhnya, Pinaki, Aparajita, Tryam-baka, Mahesvara, Vrsakapi, Sambhu, Harana and Isvara. Different Puranas give different lists of eleven names.-Tr,] I am Sankara, ... (Gambhirananda)

Lord Shankara is probably supreme among them, yet different from other Rudra-s.

These Rudra-s are existent in every cycle of Brahma.
I am not aware of their duties though.

Answer 4

Please note that when we use the word Born its not in the sense of physical birth. Its manifestation. In Vedas the diversity in counting Rudras is taken into consideration during the Yajñá in the discussion. For example:

1. Kṛṣṇa Yajur Vedā Taittirīya Saṃhitā 1.4.11 states “three and thirty in troops”; at the same time it says “eleven are seated on waters”.
2. When Vedic meter is considered, Rudras are associated with Triṣṭubh which has 11 syllables multiplied by 4 steps, hence Śrī Rudram of the Kṛṣṇa Yajur Vedā describes 11 homages to Rudra.
3. Similarly, Śatarudriya of the Sukla Yajur Vedā mentions 6 Rudras with Triṣṭubh and gives 6 X 11 = 66 homages to 100 Rudras. The same Śatarudriya 16.54 states that Rudra manifests in all and so there are innumerable thousands of Rudras.
4. Yoga of Ṛṣi Vaśiṣṭha describes 100 Rudras, whereas the Mahabharata Itihāsa in its Drona Parva-Narayanastra-mokshana Parva 203 says “Infinite Rudras”.
5. When offering of sacrifice during Yajñá is in the discussion, Atharva Veda 15.5 talks about 7 intermediator/intermediate spaces in different directions – Bhāva to the Eastern, Śarvā to Southern, Paśūpati to Western, Ugra/Aghora to Northern, Rudra towards nadir or below regions, Mahādeva to the upper regions of the sky/zenith and īśhana towards all directions.
6. When associated with the human body, Sharva (Śarvā) is associated with the kidneys, Bhāva with the liver, Rudra with the blood and the liver, Paśūpati and Agni with the heart, Mahadeva with the intestines and Ugra/Aghora with the stomach/gut TS1.4.36.
7. Vājasaneyi Saṃhitā of the Sukla Yajur Vedā describes 6 aspects – Bhāva, Rudra, Śarvā, Paśūpati, Nilagriva and Śitikaṇṭha.
8. When Rudra is associated with Liṅga then five aspects are described – Sadyojata, Vamadeva, Aghora, Tatpurusha and īśhana.
9. Rishi Yagnavalkya in Brihadaranyaka Upanishad, attributes the 10 vayus (prânas), and 11th as the Âtman are all Rudras.Various Anuvākam with their respective meters/syllables make up the mantra, using which various manifestations of Rudras are appeased in Yajñá. For example, Virād meter is of 10 syllables used to give oblation in 10 directions to 10 prāṇas which provide full life called āyus. Taittirīya Saṃhitā 4.5 talks about 1000 Rudras covering the Earth with 100 bows and 100 arrows. So, here is the key: depending on the cause and the event, the concept of Rudra manifests. This is the reason why He is called Viṣvarūpam or Pururūpam (the universal or cosmic form with multiple flavors) RV 2.33.10/TA 10.23.1. Śrī Rudram and Śatarudriya presents totality of Rudra’s omnipresence (which we will explore soon) – especially Taittirīya Saṃhitā 1.8.6, which says “एक एव रुद्र न द्वितीयाय तस्थुर्” meaning “There is only One, Rudra without a second”. This, in turn, gave a foundation to the Svetasvatara Upaniṣhad (one among the 18 primary Upaniṣhads), which says in Chap 3, sloka 2. However, when it's common for human intellect to iconify names like Rudra and limit such name with an image, but we saw how Rudra is not a person or a creature or to iconify. Its clear from the event of Bhutavan in Rig Vedā wherein a nameless divinity arises, and again in Sukla Yajur Vedā Śatapatha Brāhmaṇa a nameless boy emerges from Prajāpati's Yajñá and enter into 8 forms which is famously known as the Astamurti tatva, and Prajāpati says that the boy is not a mere boy (kumara) and even after searching He was no where to be found (Apaśyat) yet one can find Him in these eight forms (Rudra, Sarva, Paśūpati, Ugra, Aśani, Bhava, Mahādeva & īśhana). Rudra is a nameless divinity, there is no form or name (nama rupa), that is why the worship of Siva is of a linga which is arupa-rupi. But what better than an analogy from Chandogya Upaniṣhad Chap 6:

एको हि रुद्रो न द्वितीयाय तस्थुर्य इमांल्लोकानीशत ईशनीभिः। प्रत्यङ्जनांस्तिष्ठति सञ्चुकोचान्तकाले संसृज्य विश्वा भुवनानि गोपाः॥ There is (हि) The One (एको ) Rudrā (रुद्रो) and none (न) other than He, none can make Him second (द्विती) in being (याय) that is in existence (तस्थु:र्य) among the worlds( इमां:ल्लोका), He is the authority (ईशते) by His own authority (ईशनीभिः)| In all worlds/dimensions (भुवनानि) is His convolution and projection and guardians (संसृज् + ज्य + गोपाः) in entirety (विश्वा), He is established (तिष्ठति) in all beings (हे जनाः) as the indweller (प्रत्यङ्); and all beings (भूत्वा), at the time of final dissolution (अन्त:काले), become/withdraw into Him (सञ्चुकोच) ~ Svetasvatara Upaniṣhad 3.2

सदेव सोम्येदमग्र आसीदेकमेवाद्वितीयम् । तद्धैक आहुरसदेवेदमग्र आसीदेकमेवाद्वितीयं तस्मादसतः सज्जायत ॥6.2.1 कुतस्तु खलु सोम्यैवंस्यादिति होवाच कथमसतः सज्जायेतेति। सत्त्वेव सोम्येदमग्र आसीदेकमेवाद्वितीयम् ॥ 6.2.2 यथा सोम्य मधु मधुकृतो निस्तिष्ठन्ति नानात्ययानां वृक्षाणांरसान्समवहारमेकतांरसं गमयन्ति ॥ 6.9.1 ते यथा तत्र न विवेकं लभन्तेऽमुष्याहं वृक्षस्य रसोऽस्म्यमुष्याहं वृक्षस्य रसोऽस्मीत्येवमेव खलु सोम्येमाः सर्वाः प्रजाः सति सम्पद्य न विदुः सति सम्पद्यामह इति ॥ “from a single ball of clay, we can know every form made of clay, the difference in form is but the name (nama-rūpa). In the beginning was one being, without a second, or non-being, without a second; and from that various beings came to be. Just like bees make one honey from nectars of various flowers, yet the honey do not know from which tree or flower, in the same way, all beings begotten from One Being do not know their source” Please note: the word “Being” doesn’t mean a person nor an alien or animal, beings means “to be” or “to exist”. Existence can’t be described or iconified with in image/form within the frontier of vocabulary. ~ Chandogya Upaniṣhad 6.2.1/6.2.2/6.9.1/6.9.2

For more detailed information please google "Sanatanadhara Siva Rudra across Vedas and Itihasa"