As the Oxford Dictionary states
"The action or offence of speaking sacrilegiously about God or sacred things; profane talk
and the Merriam Webster Dictionary as
Irreverence toward something considered sacred or inviolable
and most appropriately by the same Dictionary as
Blasphemy is the act of insulting or showing contempt or lack of reverence for deities, to religious or holy persons or things, or toward something considered sacred or inviolable.

Status of Blasphemy in other religions

Among Jews and Christians, the "Book of Leviticus" (Old testament) states that

"The Jewish law is based on the case of the blasphemer, one of the mixed multitude that went out of Egypt with the children of Israel (Lev. xxiv. 10-23). He blasphemed the name of the Lord and cursed; was sentenced to be taken without the camp; and it was decreed that all who heard him should lay their hands upon his head, and that all the congregation should stone him. The judgment in his case was formulated in a general law in verses 15 and 16."

What if any heathen has done a blasphemy, or any Jew has abused the names of heathen gods?

Although, according to Jewish law, a Jew who blasphemed a heathen deity was not guilty of the crime of blasphemy, Josephus ("Ant." iv. 8, § 10, after Philo, "Vita Mosis," 26; ed. Mangey, ii. 166) to the contrary notwithstanding, yet a heathen might be guilty if he blasphemed the name of the Lord (Baraita Sanh. 56a). The crime of the heathen blasphemer, though subjecting him to the penalty of death, did not oblige the Jewish by-standers to rend their garments. The Talmud bases the custom of rending the garments in such cases upon the Biblical precedent in II Kings xviii. 37)

Means if any Jew has done the crime, he will not be punished and on contrary to it, if any heathen has done the crime, he will be punished.

In Hinduism their is no such consistent law is present.

In Buddhism, it speaks about the reaction of Lord Buddha if someone used to insult him. According to it, the Lord Buddha appreciated to not indulge in such discussion or even if any such thing happens, forgive them.

Status of Blasphemy in Islam

There is no clear verse present in Quran and no Hadith of Holy Prophet (PBUH) is present which can describe the punishment of Blasphemy.
In Sunnah one such example is present

The Prophet said, "Who is ready to kill Ka'b ibn al-Ashraf who has really hurt Allah and His Apostle?" Muhammad bin Maslama said, "O Allah's Apostle! Do you like me to kill him?" He replied in the affirmative. So, Muhammad bin Maslama went to him (i.e. Ka'b) and said, "This person (i.e. the Prophet) has put us to task and asked us for charity." Ka'b replied, "By Allah, you will get tired of him." Muhammad said to him, "We have followed him, so we dislike to leave him till we see the end of his affair." Muhammad bin Maslama went on talking to him in this way till he got the chance to kill him. Narrated Jabir bin 'Abdullah
— Sahih al-Bukhari, 4:52:270, see also Sahih al-Bukhari, 5:59:369, Sahih Muslim, 19:4436 Sahih al-Bukhari, 3:45:687 Sahih al-Bukhari, 4:52:271

But this is just one example (having two facets as well) as against dozens in which Holy Prophet (PBUH) forgiven all

1. Stoning of Holy Prophet PBUH by Taif hooligans.
2. Garbage thrown by an Old Lady.
3. Hide of dead animal thrown on him while praying.
4. Abusing him with words like "Majnoon" ""Fabricator" "Liar". There are nearly 200 places in Quran but along with them there is no punishment present.

In all such cases Holy Prophet (PBUH) forgiven the culprits and not only forgiven but prayed for their forgiveness from Allah and to show them the right path...

Stance of Ehl-e-Sunnat WalJamaat

State is responsible for the punishment of such people according to the law. Individuals are not allowed to take the law in their hands according to Shariah. There will be investigation regarding this and if the person in question is found guilty, he or she will be sentenced to death by the state.

Case of Ka'b ibn Al-Ashraf

He was a Madiniite and there was a treaty among the people of Madina that there will be no collusion with the Makkahns.
Ka'b ibn al Ashraf has colluded with Makkahns, taken money from Abu Sufyan to mock the Holy Prophet PBUH and the martyred Muslims.
His murder was more political then personal in nature.
One more cause of his murder is said to be when all Jewish tribes were accused for treason against the state of Madina. And for treason there is always a sentence of death in every religion,nation and country even in the present time.

Muslims' Unjustified reaction towards Blasphemy

Firstly

Individually or in a mob the lynching of any person accused of blasphemy is not allowed and state is responsible for punishment.

Secondly

There are certain sects among Muslims as well in which there is a practice of "Organized Blasphemy" (as the definition implies) against the sacred personalities of religion. And the followers of such sects are in millions.

There are dozens of books written by Authentic and reverend Muslim (Both Shia and Sunnis) Scholars in which there are certain sentences which can be taken as clear "Blasphemy" against even "Holy Prophet PBUH"...And the followers of such scholars are in millions as well.

When there are wolves in our hordes then why we are blaming people of other religions, ignorant to our traditions and customs?