Islam has the concept of martyrism. Do any Hindu scriptures have a similar concept? If not is there anything close?
Yes , there is a concept of Martyrism in Hinduism scriptures.This concept is described in a story in Shreemad Bhagvat Purana.
Background - This story is of a demon "Vruttasura" Rushi (sage) Dadhichi, Indra & Demigods.In this story demon "Vruttasura" hide all the weapons & powers of demigods.Then Indra (King of demigods) and all gods seek refuge of the Supreme Lord. He instruct's them to build a weapon from bones of Sage Dadhichi.In this war when Vruttasura see that all his demon solder's are leaving the warzone he says to them that " It's better to die in warground (battlefield) , in that case one gets the Swarga (Heaven) by fighting bravely in battfield and dies there fighting.
These are the sanskrit verses from Bhagvat Puran -:
दवौ संमतविह मृत्यु दुरापौ यद् ब्रह्मसंधारणाया जितासु:।
कलेवरं योगरतो विजह्याद्य यदग्रणी र्वीरशयेs निवृत: ॥33॥
dvau sammatāv iha mṛtyū durāpau yad brahma-sandhāraṇayā jitāsuḥ kalevaraṁ yoga-rato vijahyād yad agraṇīr vīra-śaye ’nivṛttaḥ
Meaning - There are two ways to meet a glorious death, and both are very rare. One is to die after performing mystic yoga, especially bhakti-yoga, by which one can control the mind and living force and die absorbed in thought of the Supreme Personality of Godhead. The second is to die on the battlefield, leading the army and never showing one’s back. These two kinds of death are recommended in the śāstra as glorious.
जातस्य मृत्युर्ध्रुव एष सर्वतः प्रतिक्रिया यस्य न चेह क्लुप्ता ।
लोको यशश्चाथ ततो यादिं ह्यमुं को नाम मृत्युं न वृणीत युक्तम् ॥ 32॥
jātasya mṛtyur dhruva eva sarvataḥ pratikriyā yasya na ceha kḷptā loko yaśaś cātha tato yadi hy amuṁ ko nāma mṛtyuṁ na vṛṇīta yuktam
Meaning - Vṛtrāsura said: All living entities who have taken birth in this material world must die. Surely, no one in this world has found any means to be saved from death. Even providence has not provided a means to escape it. Under the circumstances, death being inevitable, if one can gain promotion to the higher planetary systems and be always celebrated here by dying a suitable death, what man will not accept such a glorious death?
And this martyrism concept is also clearly stated in Shiva Mahapurana
- Uman samhita chapter 21 - shloka 25 – Page 83
यस्तु शस्त्रमनुत्सुज्य म्रियते वाहिनीमुखे |
संमुखो वर्तते शूर: स स्वर्गान्न निवर्तते ||२४||
One who dies in battleground , holding a weapon , such a warrior never returns from the heaven.
Martyr is (as a noun)
a person who is killed because of their religious or other beliefs.
or (as a verb)
kill (someone) because of their beliefs.
There is not exactly something like that in our Shastras but to your question is there anything close? i have an answer.
In Sanatana Dharma or Hinduism both Brahmins and cows have exalted positions.They are both considered Holy and the holiest among their kinds.
Killing a Brahmin or a cow are both grave sins with the former being listed among the 5 gravest sins(5 Mahapatakas) in all Hindu scriptures.
Manu Smriti 12.55. The slayer of a Brahmana enters the womb of a dog, a pig, an ass, a camel, a cow, a goat, a sheep, a deer, a bird, a Kandala, and a Pukkasa.
Manu Smriti 9.235. The slayer of a Brahmana, (A twice-born man) who drinks (the spirituous liquor called) Sura, he who steals (the gold of a Brahmana), and he who violates a Guru’s bed, must each and all be considered as men who committed mortal sins (mahapataka).
Now, the same Shastras say that if someone sacrifices one's life while saving a Brahmin or cow commits a great punya(an act of great merit).Similar is the case when that person does not die but saves the cow or the Brahmin.
Manu Smriti 11.79. He who unhesitatingly abandons life for the sake of Brahmanas or of cows, is freed from (the guilt of) the murder of a Brahmana, and (so is he) who saves (the life of) a cow, or of a Brahmana.
The exact verse is found in the Parashara Smriti as well.
I don't know if i have answered your question or not but these are the closest examples i found from Hindu Shastras that talk about "sacrificing life for saving religion,or for the sake of religious beliefs"
Martyr -- A person die fighting in battle against enemies.
I am putting this definition, because if a policeman dies in street fights, then they are usually not termed as martyrs. The "enemy" part is essential.
There are numerous references of "martyrdom" and how a "Kshatriya" (armyman in this context), dying on battlefield attain heaven. Very famous reference is there in Bhagavad Gita itself. (GambhirAnanda's translation):
BG 2.32 - O son of Partha, happy are the Ksatriyas who come across this kind of a battle, which presents itself unsought for and which is an open gate to heaven.
BG 2.37 - Either by being killed you will attain heaven, or by winning you will enjoy the earth. Therefore, O Arjuna, rise up with determination for fighting.
However, there is a small caveat here. Not everyone dying on battlefield may attain heaven. For example, if a running away soldier is chased to death, then it's a cowardly death.
Hence, the qualities of good Kshatriya are described here:
BG 18.43 - The natural duties of the Ksatriyas are heroism, boldness, fortitude, capability, and also not retreating from battle, generosity and lordliness.
On the side note, despite knowing all these, the great warrior Arjuna was still not convinced to fight. Because, heaven or material pleasures were no longer attractive to him. Hence, even though Krishna first tries to convince him with such 'benefits', Gita doesn't stop at heaven/earth/hell etc..
The supreme abode is beyond all the planes of material world. However, that's out of context for this Qn.
Most of the answers have taken an inward focus without taking into consideration OP and his specific tag
other-religion. Let me elaborate this aspect a bit more...
Indeed, being a religion which faced religious onslaught for several centuries, Hindus have internalized martyrdom and incentivised dying for the righteous (dharma), country (desha). Previous answers have elaborated sufficiently on this.
Now the differences,
Rajiv Malhotra writes,
In Hinduism, there is no concept similar to Christian martyrdom or Islamic jihad. The most important and revered historical figures of Hinduism were not martyrs. Spirituality is not about fighting someone or some religion. There is no discussion of other religions in Hindu scriptures, no campaigns against "false gods." Comparative religion is not of much interest to Hindus, as they do not see religion through competitive or predatory eyes. Comparative religion is not of much interest to Hindus, as they do not see religion through competitive or predatory eyes. Christians, on the other hand, go out of their way to control positions in academics, to research and to teach about Hinduism, as a sort of competitor intelligence gathering which seeks hegemony.
Indeed, when faced with aggression, Kshatriya is supposed to do his duty to protect dharma (righteous), praja (people) and desha (country).
On the contrary, in the book, "God against the Gods", by Jonathan Kirsch, he gives the history of early Christianity's focus on encouraging martyrdom for gaining religious merit.
These zealous Christians were encouraged to provoke fights in order to become martyrs. This kind of behavior was broadcasted in order to encourage more persons. Such martyrs were celebrated, honored, and many of the thousand of saints were recognized primarily for their martyrdom. To fight infidels became seen as the highest sacrifice for God. In-fact, Jesus is considered the first martyr.
Also, in The Calcutta Quran Petition by Sita Ram Goel describes how the very fact that a shahid (martyr) has the highest place reserved in the Islamic heaven. Higher even that a Ghazi (Islamic warrior) shows the relevance and importance of martyrdom in Islamic tradition. The anecdotal 72 virgins as a reward for martydom is specified in Hadith. It says,
That the Messenger of Allah said: "There are six things with Allah for the martyr. He is ... married to seventy two wives along Al-Huril-'Ayn of Paradise, and he may intercede for seventy of his close relatives."
So, all in all Hindus do respect the martyr, but there's no great place reserved for him in the path to moksha. He may enjoy the fruits of his self-less duty by spending some time in svarga (heaven) but will soon return to the Earth as reincarnated soul.