According to MIPT website, there had been 84 incidents involving ASALA leaving 46 people dead, and 299 people injured including the following:

February 16, 1976 in Turkish Embassy in Beirut, Oktar Cirit was killed.
October 12, 1979 in Turkish Embassy in the Hague, Ahmet Benler, the son of the Ambassador Özdemir Benler, was killed (This attack was one of the attacks co-claimed by JCAG.
July 31, 1980 in Turkish Embassy in Athens, Galip Özmen and his 14 year old daughter Neslihan were killed in the Turkish consulate. Galip Özmen's wife Sevil Özmen and their son Kaan survived the attack with injuries.
December 29, 1980 in Madrid, a Spanish journalist, assistant director of the "Pueblo" newspaper, José Antonio Gurriarán was accidentally injured during an October 3 group attack. Then Gurriarán was interested what the group's purposes were; he found and interviewed ASALA members. In 1982 his "La Bomba" book was published, dedicated to the Armenian cause and Armenian militant's struggle.
March 4th, 1981 in the Turkish Embassy in Paris, Reşat Moralı was killed and Tecelli Arı was injured.
June 9th, 1981 in the Turkish Consulate in Geneva, Mehmet Savaş Yergüz was killed.
September 24, 1981 in Turkish Consulate in Paris, 56 Turks were held hostage in the embassy by ASALA militants (none of the hostages were harmed), Turkish guard Cemal Özen was killed. ASALA members demanded the Turkish government free Armenian political prisoners within 12 hours and fly them to Paris. After 15 hours they surrendered peacefully requesting political asylum from the French government.
April 28, 1984 in Turkish Embassy in Tehran, Iran, Işık Yönder was killed.
The ASALA's most criticized attack was on August 7, 1982 in Ankara at the Esenboğa International Airport, when its members targeted both militants and non-diplomat civilians for the first time. Two militants opened fire in a crowded passenger waiting room. One of the shooters took more than 20 hostages while the second was apprehended by police. Altogether, nine people died and 82 were injured. The arrested militant Levon Ekmekjian condemned the ASALA in the aftermath of the attack and appealed to other members to leave and stop the violence. The Esenboga attack also precipitated a split in the group over tactics, between the Nationalists (ASALA-Militant) led by Hagopian and the 'Popular Movement' (ASALA-Mouvement Révolutionnaire) led by Monte Melkonian. While Melkonian's faction insisted on attacks strictly against Turkish officials and the Turkish government, Hagopian's group disregarded the losses of unintended victims and regularly executed dissenting members. On August 10, 1982, Artin Penik a Turkish-Armenian, set himself on fire in protest of this attack.

Prominent Armenian poet Silva Kaputikyan in 1983 wrote "Its raining my sonny" poem dedicated to the memory of ASALA member Ekmekjian.

On July 15, 1983, the ASALA carried out another attack at the Orly Airport near Paris, in which 8 people were killed. The attack gave the group a new nickname, the Orly Group. Afterwards, French forces promptly arrested those involved.

ASALA
Attacks by ASALA

Source: Wikipedia