A wide variety of weapons is used, but not many are named. Weapons that didn’t make the list are:
-axes (wielded most notably by dwarves, Tuor, Húrin father of Túrin, and Gothmog the Lord of Balrogs),
-daggers/knives, the most famous of which is Angrist that cut the Silmaril from Morgoth’s crown,
-bows, the most famous of which is Belthronding, the large black bow of Beleg Strongbow, a great Elven archer of Doriath.
Anglachel / Gurthang [‘ahn-glah-khel / ‘goor-thahng] (“Iron of Death”)– a black sword made of meteoric iron; the only recorded sword to have produced a voice; probably the most famous creation of Eöl the Dark Elf; its most famous owner was Túrin Turambar, who chose one of his names after the sword (Mormegil- Black Sword); used to kill Beleg, Glaurung the dragon, and others; Túrin ended his own life with it; buried with Túrin.
Ringil [‘rin-gil] – sword of Fingolfin, High King of the Noldor in Midle-earth; used in his duel with Morgoth whom it wounded, and caused him to limp ever since.
Narsil [‘nahr-sil] – the sword of Elendil; shone with the light of the Sun and the Moon; it broke as Elendil fell in the combat with Sauron in the Last Alliance; its shards cut the Ring from Sauron’s hand, and were later on kept in Rivendell until the sword was reforged as [b]Andúril[/b].
You know it from: the entire LotR series.
Also around in the First Age were three blades made in Gondolin- Glamdring (carried first by Turgon the King of Gondolin, later by Gandalf), Orcrist (carried later by Thorin Oakenshield), and Sting (short sword later carried by Frodo and Bilbo by whom it was named).
Grond (“the Hammer of the Underworld”) – the mace of Morgoth; appears only in his duel with Fingolfin; it’s so large its stroke creates a large pit in the earth.
Aiglos (Aeglos) [‘eye-gloss] (“Snow-point”) – the spear of Gil-Galad; used in the final combat against Sauron.
You know it from: it’s mentioned in Sam’s song of Gil-Galad on Weathertop, and by Elrond during the Council as he narrates the history of the Ring. (FotR)