Does any of the Gods or Goddesses ever cry even up to this very day like we humans do?
Brahmavaivarta Purana, Krishna Janma Khanda, Chapter 43, refers to Lord Shiva crying and lamenting the death of Dakshayini alias Sati.
Shiva was in such a deep grief that he is in literal tears due to pain of separation from Sati.
Lord Vishnu had to literally hold Shiva and console him. By grace and words of Lord Vishnu, Shiva's pain was reduced and peace returned to Shiva.
In Valmiki Ramayana, in Aranya khanda, Canto 58 onwards, Sri Raama laments and cries due to kidnapping of Sita by Ravana. Raama almost starts talking to all the things like animals, trees in the forest and even requests, godavari river to tell what has happened to Sita. Valmiki says due to fear of Ravana, river Godavari didn't answer Raama. Raama due to anger says that he will destroy all the worlds.
Finally, Lakshmana, the wonderful, brother of Raama, prays to Raama and reminds him that Raama being so powerful, that he can annihilate every thing, consoles him and cools down Raama (Canto 65 onwards in Valmiki Ramayana, Aranya Khanda)
In Yuddha Kanda, Valmiki Ramayana, Canto 101, Verses 9 to 22, Raama laments when Lakshmana becomes unconscious on battlefield being hit by Shakti astra by Ravana. Raama goes to the extent of saying what is the use of victory and Kingdom, without Lakshmana.
"wives may be found and kinsmen too can be had everywhere, but not a brother like Lakshmana can be had by anyone, anywhere"
This shows Raama's deep love towards Lakshmana is unfathomable and he held lakshmana dearer than his own life.
In Srimad bhagavatham, (Dashama skandha (Book 10), chapter 77, verse 22 onwards) there is only one incident where Lord Krishna laments. When fighting Salva, Salva creates illusory vasudeva (father of Lord Krisha) and executes him. Seeing this Lord krishna for a moment laments then immediately sees through the illusion of salva and eliminates salva with his chakra Ayudha. This act of Lord Krishna is considered to be a leela.
Its difficult to answer straight forward because it involves different ways of looking and believing god
1) If we see from the angle of Puranas, then answer is Yes. We have lots of references. One example is Suchi, the queen of former Indra cries, for help when new Indra Nahusha lust for her. You can read the story here.
2) If we see God from Vedantic perspective, then answer is unknown. Because he is everywhere. In a drop of water, even in sad and happiness. Because he is Vishwaroopa. Refer here
3) If we look from the angle of Swarga Loka , then no Gods/Godess will ever cry there because it is the paradise of pleasure.
So answer to this question depends on the belief you follow and the philosophy close to your heart.
Also cry can be classified into many types, primarily due to Sad and extreme happiness. So 'Cry' in above question refers to what needs clarity.
Following are some instances which I can think of. I will extend the answer if I find more details.
- Rudraksh tree and its beads actually emerged out of tears of Lord Shiva when he saw that Tarakasur's sons are again turning towards Adharma. According to wikipedia article on Rudraksh
Creation of the rudraksha tree from the tears of grief shed by Shankar (or Shiva) upon seeing the unrighteous conduct of demon Tarakasur’s sons, and their destruction by Shiva :
"Through their righteous conduct and devotion unto Shiva, Tarakasur’s sons Tadinmali, Tarakaksh and Kamalaksh, attained divinity. After some time, seeing that they have returned to their original unrighteous conduct, Shankar was grief-stricken, and His eyes were filled with tears. A few of these tears fell onto the earth; a tree sprang up from these, which came to be known as the rudraksha tree. Later, Shiva destroyed the sons of Tarakasur." -Gurudev Dr. Kateswamiji
- In Ramayana, when Ravana kidnapped Devi Sita, Lord Rama cried during the time he was searching her. Sorry but I don't know where it is written in Ramayana but I think it is there. I think there might be some other instances also in Ramayana, like when he heard the news of death of King Dashrath, or when Lakshaman became unconscious by Meghnad's arrow, or when Devi Sita got submerged in the earth. There might be some other instances in Ramayana as well.
There is one account of great god Lord Mahadeva's or Shiva's eyes filled with tears in compassion for a deceased child . This story is present in Mahabhrata Shanti Parva- Apaddharmanusasana Parva- Chapter 153.
There is a story in Mahabharata about relatives of a deceased child ,who died early in his childhood and vulture and Jackal. The relatives of boy was in great grief about the early death of their single boy , on cremation ground a jackal and vulture finding an opportunity to eat discuses the reality with them. And the vulture told them that great gods can revive him , they only have the power and compassion to do so. And then Lord Shiva seeing the grief of the relatives comes there with goddess Uma and gives anew life to dead boy. The moral of the story is god is great he can do anything and death is certain who has born , but the exception is god.So we should not be great grief over the death. And gods including Lord Shiva is having great compassion towards men. When Lord Shiva comes to cremation ground near the relatives of the boy his eyes gets filled with tears with compassion over looking at the grief of relatives and the dead boy.
तथा तयो विर्वदतोर्विज्ञानविदुषोर्द्वयो: |
बान्धवानां स्थितानां चाप्युपातिष्ठत शङ्कर : ||110 ||
देव्या प्रणोदितो देव: कारुणयार्द्रिकृतेक्षण: |
ततस्तानाह मनुजान् वरदोsस्मिति शङ्कर : ||111 ||
P. 341 While the bird and the beast, both possessed of wisdom.. were thus disputing and while the kinsmen of the deceased child sat listening to them, the great god Sankara, urged by his divine spouse (Uma), came there with eyes bathed in tears of compassion.
Here Lord Shiva is not crying just like us , but its the tears of his great compassion and kindness towards all.