The Astral Vine spell temporarily charges an object with magical energy so that it can hurt mazoku - it's frequently used by Zelgadis to enhance his sword. Amelia invented a similar spell, Visfarank, which affects the caster's hands and feet.
In Fairy Tail, all the magic in Edolas comes in this form, however Edolas magic/weapons are of significantly lower quality than Earthland magic (The flame staff can only do one strong attack before expiring)
The chakra-flow technique in Naruto is used by many characters to enhance bladed weapons with Elemental Powers.
Whitebeard from One Piece can channel his Gura Gura no Mi powers into the blade of his bisento allowing him to launch massive shockwaves from it or hit with literal explosive force.
Haki users can channel their Busoshoku Haki into their weapons, i.e. swords, arrows, etc., allowing them to hit harder or harm Devil Fruit users.
In Immortal Iron Fist, turns out that past Iron Fists have had the ability to channel the chi of Shou-Lao the Undying into their weapons, be they a bow and arrow or a pair of pistols. Honestly, the standard use of the Iron Fist may count, only in that case the "weapon" is the user's own fist.
Warhammer: Wizards using the Lore of Fire can cast Flaming Sword of Rhuin, which enhances the weapons of the troops targeted with it by setting the edges on fire. Wizards of Metal can use Enchanted Blades of Aiban to make troop's weapons into Absurdly Sharp Blades.
The arcane spell "Magic Weapon" and "Greater Magic Weapon" which enchant a weapon with a +x to attack/damage. A druid can do the same thing to natural weapons (claws, etc.) with the "Magic Fang" line of spells. Other spells exist to bless a weapon (for fighting evil creatures), turn it into a specific metal (such as silver to fight lycanthropes), or even turn it into Pure Energy that passes through non-living material like armor. Psionics gets in on the action with "Metaphysical Weapon/Claw" and "Weapon/Claws of Energy".
Also the "Mighty Wallop" line of spells, which make bludgeoning weapons hit as if they're x times bigger than the actually are.
The artificer's "Weapon Augmentation" infusion does this, allowing him to temporarily imbue a weapon with the abilities of any magical weapon.
The paladin spell "Holy Sword" and the Eberron cleric spell "Heroes' Blade" turn a sword into a holy blade for a ton of bonuses and awesomeness.
The duskblade takes a different approach, with the ability to cast spells on enemies as they strike them with their weapons. The arcane archer and enlightened fist Prestige Classes get more limited versions based on arrows and fists respectively.
Many of the spells cast by 4e's Swordmage are at least flavored this way.
Pathfinder, being based on Dungeons & Dragons 3.5, shares most of its examples. The magus class combines duskblade-style spell channeling with the ability to grant temporary enchantments to its weapon.
The Legend System not only has the basic Flame Blade spell, but the tactician class also has one that lets their allies' weapons cut away magical buffs.
Also, this is pretty much the entire point of the Just Blade track.
Seiken Densetsu 3 has various "Saber" spells, which can be used on not only the user, but their allies as well. There is one Saber spell for all 8 elements, with Moon Saber letting you absorb the enemy's HP and Leaf Saber absorbing MP. Duran and Charlotte can learn most of these spells, and Kevin can learn a few as well depending on what class you make him. There are also items that can replicate the effects of these spells. Some bosses will even deliberately cast a saber on you of an element that they absorb.
In Tales of Symphonia, Sheena learns spells like this every time she forms a pact with a summon spirit (Tethe Seal or Sylva Seal, depending on which world the Spirit resides in). The spells would temporarily give one person's weapon the elemental properties of the spirit in question. There are also items called "Quartz" that have the same effect when used in battle.
In Eternal Darkness, the characters can enchant any weapon from various periods of history. This ends up with the situation where you can have an enchanted assault rifle with attached grenade launcher.
Warhammer Online: Based on the tabletop version above, Empire Bright Wizards can cast Flaming Sword of Rhuin to set the edges of his party's weapons on fire. Dark Elf Sorcerers can give their party's weapons ice upgrades.
Fable brings us augments, some of which can upgrade their weapons with elemental power like fire and electricity.
Several mage abilities in Dragon Age: Origins add elemental damage/effects to your entire party's weapons.
In Magicka one of the options you have in spellcasting is to channel your spell through your melee weapon.
Dual techs between Crono & Marle or Lucca in Chrono Trigger produced this effect.
This ability is a trademark of Shamans in World of Warcraft, used to improve a weapon's melee speed, spellcasting power, or healing power.
Expanded upon in Cataclysm, where Shamans gained the Unleash Weapon (which can now also be extended to Unleash Fury at level 90) spell, which activated certain effects depending on the currently active weapon enchants.
In the fifth and final Legacy of Kain game Defiance, Raziel gains multiple elemental upgrades for his Wraith Blade to eventually meet his destiny.
In League of Legends there are several items that qualify for this, including items labelled "spell blade" which after you use an ability makes your next attack deal bonus damage based on either your base attack damage or your ability power. Others simply add bonus magic damage to your attacks. A number of champions also deal magic damage on their attacks without items as a result of their abilities. For example, Orianna deals bonus damage increased by her ability power, which deals more damage when she hits the same target multiple times in a row.