Berserk: After the party meets Flora, Isidro and Serpico get a fire dagger and a wind rapier respectively. Schierke also wanted to give Guts a (presumably) earth-elemental axe, but he preferred to stick with his Dragonslayer.
In Bleach, there are a few spiritual weapons which are elemental in nature. However, while most merely emit the element in question, some weapons play with this trope.
Rukia Kuchiki has an ice-and-snow type weapon, which normally means controlling the element. But, if the sword happens to break, she can recreate a new one from ice.
Captain Toshiro Hitsugaya's sword both emits ice, snow, and freezing water, and absorbs moisture from his environment. It also has a weakness in that it will slowly wear away the more he uses it. However, ample moisture and cold allows him to replenish the sword and its power. This creates something of a stalemate when he goes against Tier Halibel, whose sword also absorbs and controls water, but can also melt ice. Even later still, when his commander releases his fire-type weapon, Hitsugaya states that he is unable to use his sword at all because all of the moisture has been completely dried up, and his ice would melt instantly.
And speaking of him, when he releases bankai (final form), Captain Yamamoto's sword becomes flame itself. Instead of being wrapped in flames like in its shikai (initial form), the blade becomes one with them. Merely touching the blade at that point will cause its victim to go "poof".
Tales of the Lance. A Frostreaver is a heavy battle axe made of ice gathered from a secret location on Icewall Glacier. One full day of above freezing temperature or 1-6 hours at warm temperatures (50 degrees Fahrenheit) causes the Frostreaver to melt.
Module Rary the Traitor. Lord Robilar wields the Blade of Black Ice, which was created by the demigod Iuz himself out of ice.
Legends & Lore.
The avatar of the Japanese deity Ho Masubi has a sword made of fire. It does 10 extra Hit Points of fire damage per hit and if the target is wearing armor, the armor must save vs. magical fire or be destroyed.
The avatar of the Hindu deity Brihaspati carries a bow that fires arrows of brilliant light that can render the target blind for 1-10 days.
The avatar of the Hindu deity Indra has a bow that fires lightning bolts that do 2dl0 points of damage and have a range of 1,000 yards.
Deities & Demigods Cyclopedia. The Native American deity Hastsezini has a lance made of fire and a bow that can shoot arrows made of fire.
Dragon magazine #127. The bow Ice Fang can create and fire arrows of ice out of water vapor in the air. The arrows do double damage against creatures that use or dwell in fire. In temperatures of 120 degrees Fahrenheit or higher the arrows have half normal range.
Gods, Demigods, & Heroes. The Norse Mythology deity Valis had a shortbow that could fire an arrow of lightning.
In Borderlands (and its sequel), guns and grenade mods can have elemental damage. This gives them a damage bonus (with a chance for DOT) and makes them more effective against certain targets. The first game had corrosive/acid (armour), fire (flesh), shock (shields) and explosive (basically "non-elemental" bonus damage). The sequel added slag (no bonus damage on its own, but it applied a debuff which made the target weaker to everything else). Shields similarly had damage resistance (and some also had effects which dealt elemental damage, such as harming enemies that used melee attacks).
A staple of Diablo games. They can come with elemental powers themselves or can be given some through socketing.
In Dragon Age: Origins, the spells Flaming Weapons and Frost Weapons apply corresponding elemental damage bonuses to the entire party's weapons when cast.
In Dragon Age II, these spells are rolled into one, Elemental Weapons. Which elemental effect is applied to weapons depends on the elemental type of the caster's Magic Staff.
Dragon Quest IX has the Armamentalist vocation, whose specialty is imbuing a party member (and later the entire party) with the power of fire, frost, wind/lightning, earth/darkness, and life. Not only do they do more damage, but they also become resistant to attacks of that type (very useful against breath weapons).
Final Fantasy X allows you to imbue weapons with various characteristics, including elemental (fire, ice, water and lightning) damage. As you progress in the game, these become less useful in favor of breaking the damage cap and increasing Overdrive. Tidus' iconic sword Brotherhood is the only water-elemental sword you can find for some time.
In Final Fantasy XIII and Final Fantasy XIII-2, the Synergist class has access to the En- line of abilities (Enfire, Enfrost, etc.), which give temporary elemental damage effects to other party members' weapons.
Golden Sun: The Gaia Blade (and later Sol Blade) are only equippable by Venus(earth)-type characters, and give a boost to Venus power.
Mortal Kombat has two examples involving ice people Sub-Zero (Who can create swords as well as decoys using ice) and Frost (Who makes daggers out of ice).
Amaterasu's three strongest weapons in Ōkami are Solar Flare (fiery reflector), Thunder Edge (lightning BFS) and Tundra Beads (a chain of ice energy). Said weapons also lets her use elemental brush magic corresponding to said elements without needing a source.
In Star Wars: The Old Republic, the Republic Troopers and Imperial Bounty Hunters have skills that allow them to add various elemental effects to their ammo (such as the incendiary Plasma Cells, or Ion Gas Cylinders).
Shamans in World of Warcraft can imbue their weapons temporarily with fire, lightning, ice, rock and life. Some weapons also come with a random enchant that can proc elemental damage.
In Devil May Cry, Dante can acquire Alastor, a lightning BFS, and Ifrit, a fiery Power Fist. In the third game, he can get many more: Cerberus (ice 3-pronged nunchuks), Agni & Rudra (fire and wind scimitars), Nevan (electric guitar that can shoot bats), and Beowulf (light-element gauntlets and greaves).
Azure Dreams: The player finds elemental powered weapons in the tower, they do a small dose of extra damage compared to the same power non elemental weapons. This is however a double edged blade considering that the tower plays an elemental rock paper scissors.
In the first episode of Avatar: The Last Airbender's second book, Zuko creates two daggers out of fire and uses them against Azula.
"Ninjago": The whole first season is a quest to get the four elemental weapons before the baddy does.
Fridjitzu powers in Adventure Time, which allow the user to create icy nunchaku and shurikens by using specific incantations and hand positions.
Five hats means that five tropers think it is ready to publish.
You are saying that you think this draft is ready to be published. That means the description is not ambiguous,
it doesn't duplicate an existing trope, there are at least three examples, and the title makes sense.
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