Mazinger Z has the Rust Hurricane attack, where the robot blows a wind charged with corrosive particles disintegrate the enemy. Great Mazinger has the Great Typhoon, where the robot generates an incredibly strong wind, and Mazinkaiser has the Rust Tornado, an Up to Eleven combination of both attacks.
In Naruto, there's Temari and a good percentage of the rest of the Hidden Sand Village, as well as Asuma, Naruto himself, and Danzo from the Hidden Leaf, though they all focus more on the Razor Wind aspect.
There are more concussive wind jutsus as well, like Orochimaru and Gaara's Great Breakthrough or Kakuzu's Pressure Damage. The Tailed Beasts are capable of leveling towns and causing all sorts of natural disasters just by roaring.
Kensei from the Vizard possesses a wind-element zanpakutou. His release command is "Futtobase", or "Blow it away"
Senna from Bleach: Memories of Nobody has a wind type Zanpakuto named Mirokumaru which can control wind and create tornados. She even rides on top of a tornado at one point.
In his Resurrección form, Privaron Espada 103, Dordonii Alessandro Del Socacchio, can release tornadoes/cyclones from his legs.
When Soifon activates Shunko against Yoruichi, she creates gusts of wind around herself to fight. When she fights BG9 she confirms that her Shunko form is Wind which allows her to create reiatsu tornadoes around her body.
Yaiba's Big Bad, Onimaru, wields the power of the Fujin Katana, which allows him to use tornadoes, Razor Wind, and mighty gusts of wind. Later, Yaiba himself gain this power.
Erigor from Fairy Tail can create a wall of wind that can trap enemies and even make an armor out of the wind.
Also, Wendy, who is the adopted daughter of the Sky Dragon, and therefore the Sky Dragon Slayer. She doesn't start out with many offensive abilities, but the ones she has (and gains over the series) fit this pretty well. Even her most common buff-spell makes sense for Wind-based powers: it makes those she targets move a lot faster, and they even float a bit when she first casts it.
In Magical Girl Lyrical Nanoha A's Portable: The Battle of Aces, Shamal is revealed to use mostly wind spells if she's ever forced to go on the offensive, creating wind barriers and tornadoes of various sizes.
Kazuma Yagami from Kaze no Stigma is an incredibly powerful wind mage, partially (but not entirely) because he's one of the legendary Contractors who's formed a pact with the elemental god of wind. To put that in perspective, the members of the Kannagi Clan, including his cousin, Ayano Kannagi, are highly skilled users of fire magic because their distant ancestor was a Contractor with the elemental god of fire.
The Ougi clan, and especially it's successor, Ougi Shichirou, from Kekkaishi: Flight - check, Razor Wind - check, creating giant tornadoes - check, and once, he reduced a small shrine to dust in an instant using his wind powers.
Franky from One Piece, who can use his Cyborg enhancements to fire wind with the force of a cannonball.
It is speculated by fans that Dragon has an ability connected with controlling wind or weather. When he rescues Luffy in Loguetown he is accompanied by a strong storm that saves Luffy from Buggy and helps Straw Hats escape. Wind blows away flames, opening a path to his ship for survivors from the Gray Terminal as well.
It should be noted that in the second case, the wind might be from Ivankov, judging by the shape of the blast. He is also a user of this trope, creating strong blasts of wind by winking.
Hayate the Combat Butler's 'ultimate' attack doesn't quite fit this trope, but it creates a gust of wind below him (those with skirts be warned) to propel him into the air for a powered punch.
Tabitha (or better said, Princess Charlotte Heléne de Orléans) from Zero no Tsukaima.
Takeda Shingen of Sengoku Basara is so strong, a strong enough swing from his big freaking ax has enough force to summon a giant, mook-destroying tornado on the battlefield.
Vento of the Front in A Certain Magical Index has the power over wind (enough to knock over buildings) among God's Right Seat, and her ability, God's Divine Punishment, deprives anyone who is hostile towards her of oxygen.
When Saten briefly becomes an esper in A Certain Scientific Railgun, her ability turns out to have something to do with air manipulation, demonstrated by her spinning some leaves above her palm in a miniature cyclone.
Also, Kongo's "Aerohand" ability causes whatever she touches to be violently propelled away by a rocket thruster-like gust of wind. And we're not talking about small fry; her first on-screen use of it involves lobbing a truck at two helicopters, nailing both. The rest of the battle she spends running around, throwing mooks in Powered Armor like ragdolls. Though it was kinda foreshadowed by her constantly playing around with a fan. When she really pushes herself, she can launch things into outer space!
Ouma Yamisaka wields a magic crossbow that gives him wind powers. He can use wind to launch himself through the air or create gusts that can demolish small buildings.
Accelerator can control winds due to his ability to control any vector.
Saiai Kinuhata can control nitrogen. Since nitrogen makes up about 70% of the atmosphere, she can generate air currents by controlling the nitrogen.
Inukami!: Kaoru's specialty is wind magic. Though, oddly, he invokes the "White Mountain God" to do it.
Storm from X-Men uses wind powers, among her other weather-related abilities; usually, though, just to fly.
Also, student Sofía Mantega (formerly Wind Dancer) had this power, before M-day. Among other things, she had the peculiar ability to use the wind to "carry the words" from far away, to better overhear conversations.
Windfall, one of the Masters of Disaster in The DCU.
Typhon from The Incredible Hercules is capable of causing Wind-related natural disasters like Tornadoes, Hurricanes, Typhoons, etc.
Thor can project whirlwinds from his hammer, summon them naturally, or generate them with his cape. He can use these whirlwinds to carry people safely or shield them from harm.
Hay Lin from W.I.T.C.H. has this power, manifesting in high pressure wind, air bubbles to breath under water, and lifting heavy objects or even people, and, as a side effect, being the only Guardian with the ability of flight until the New Power arc (the power-up of that arc grants all Guardians the ability to fly, but Hay Lin is noted to be both faster and higher-flying). By the New Power arc, her powers over air are so great she easily imprisoned a tornado in a box small enough to stay in a pocket.
The Wheel of Time generally averts this even though it has an elemental system, as Air is generally used for telekinesis-like effects instead of wind effects.
In Codex Alera, everyone bonds with one or more "furies" of an element, one of which is wind. Wind furies grant flight and speed to powerful crafters, but don't work well in enclosed or underground spaces, and salt hurts them. A Knight Aeris without any significant furycrafting besides wind (such as Amara) also falls straight into Fragile Speedster territory. Windcrafting is also extremely useful for spying, too, as a windcrafter can cause the air to bend light to generate impromptu telescopes or to conceal people or objects, or to generate fields to hush out noise. In one extreme case, a team of Knights Aeris actually used their ability to bend light to create a giant magnifying glass that focused sunlight into an impromptu Death Ray that swept an entire bridge clean of invading Canim.
Harry Dresden uses wind magic almost as often as fire magic, maybe even more often but to less destructive effect- except in the case of the napalm firing Renfields in Blood Rites.
Elaine, in what is almost certainly a Shout-Out to The Mighty Thor, twirls one of her foci, a chain, to summon a powerful whirlwind.
Harry does the same (with his staff) one book before, creating a tornado that picks up the debris of a battle and promptly slices/pulps a lot of very powerful creatures.
The fifth and last introduced main character from Anthony Horowitz's The Power of Five series, Scarlett, has powers over the weather, including the wind. This first manifests itself when she unconsciously brings down an awesomely powerful hurricane onto the Necropolis and, with concentration, is able to lead her friends through it unscathed.
In Devon Monk's Dead Iron, Cedar's arrival at the mine is announced by dust devils that form without any wind.
Trisana Chandler in Tamora Pierce's Circle of Magic quartets has the ability to control weather, including earthquakes, heat, lightning, and wind. When traveling to a hot country, she used her breezes to pick up rumors, cool herself, lift herself to the top of a tower, block somebody's path, etc.
In Shadow Ops, aeromancy is one of the "legal" elemental schools of magic. The school not only allows for control of wind and flight, but it also allows the aeromancer to generate lighting and control storms.
Air Masters/mages in the Elemental Masters series by Mercedes Lackey, the main ones being Nigel Barrett (Reserved for the Cat), Reginald Fenyx (Phoenix and Ashes), and Rosalind Hawkins (The Fire Rose).
Ruahks in The Quest of the Unaligned have power over air and, to some degree, weather, as well as the ability to "pop" from place to place. Unfortunately, they also tend to be, well, airheads, having extreme trouble staying focused on any one thing and having a tendency to act on a whim without really thinking.
A number of spells and prestige classes in Dungeons & Dragons, starting with Gust of Wind and Wind Wall spells.
Wind is a perfectly acceptable Estate in Nobilis, and a high-Domain Power of Air is going to be pulling this stuff a lot.
Air, here associated with the colour green, is one of the six core Matoran elements of BIONICLE and, as such, is wielded by the numerous Toa of Air. Unlike most other elements, almost no non-Toa creatures have access to wind powers.
Ōkami has the Gale brushstroke, which is obtained from Kazegami. By drawing a swirl of ink, you can create winds that blow you, your opponents, or objects around. Later, you get a Whirlwind brush technique by drawing 3 horizontal lines. Can be used for juggling enemies.
Zelda has several items that give Link wind powers:
In The Legend of Zelda: The Wind Waker, Link get a magical leaf that he can use to hang-glide, at the cost of some magic. It can also be used to make a strong blast of air. Another example is the titular Wind Waker, a magical conductor's baton that can be used to change the direction of the wind and conjure cyclones.
The Legend Of Zelda Minish Cap: Gust Jar is also dual-purpose. It is charged by sucking up air (and items and enemies), and then releases it as a blast of air. Link uses it to grab elastic mushrooms to pull himself across pits, pull the shells off of enemies, and extinguish flames.
The Legend of Zelda: Spirit Tracks: Whirlwind is a horn-thing that, when Link blows into it, he can use it to push pinwheels, push important items across chasms, and throw bombs into the resident dungeon boss.
Luc, the wielder of the True Wind Rune in the Suikoden series.
The Pokémon element to which this would be attributed is Flying. Many Flying-types are pretty fast and strong in one attacking stat or the other (usually Attack, though some like Xatu, Chatot and Togekiss have higher Special Attack), but have mediocre defenses and health (though there are a few bulky Flyers like Skarmory and Mandibuzz). Flying-type attacks generally consist of the user using its beak (Peck, Drill Peck), wings (Wing Attack, Sky Attack), talons (Sky Drop), or the air itself as a weapon (Gust, Aeroblast, Hurricane, Air Slash), with a couple being simply Flying-type variants of other moves (Brave Bird, a Flying-type Double-Edge).
Johto Gym Leader Falkner, Hoenn Gym Leader Winona, and Unova Gym Leader Skyla specialize in Flying types.
The legendary Pokemon Tornadus introduced in Pokémon Black and White is notably the first pure Flying-type, and is based on the wind god Fujin.
There's also Rayquaza from Generation III; Groudon rules the earth, Kyogre rules the seas, and Rayquaza, whose roar is enough to send the other two running, rules the sky.
Lugia, whose power is so strong that just flapping its wings can blow houses apart, has a signature move called Aeroblast, an Awesome yet Practical move (if you're willing to look past the 5 PP) that has an increased critical hit rate.
Ivan and Sheba from Golden Sun both have wind manipulation powers in their base class, though any of the playable characters can gain these powers through use of the class system. Karis, their successor in the third game, has the added benefit of wind-based healing. She is joined by Sveta, who, unlike her fellow Jupiter Adepts, actually knows what she's doing in a physical fight.
Lilica Felchenrow in Arcana Heart uses the Arcana of Wind as her default.
The Arashi orb from Onimusha gives Samanosuke the ability to use wind magic.
Misaki Kawana of Eternal Fighter Zero uses wind in many of her attacks, both to boost her movement and to pound her opponent with strong gales.
Any magic user who gets their hands on the Wind, Elwind, Tornado, Forseti, Blizzard, Aircalibur, Excalibur, or Rexcalibur tomes in Fire Emblem.
Some examples of characters who wield said tomes constantly: Lewyn (Elwind and late Forseti), Lewyn's magic user children (either Corple, Arthur or Ced) (Forseti), Cecilia (Aircalibur), Ursula as a morph (Excalibur), Soren (Rexcalibur), Ricken and later Laurent (Elwind)...
Both shamans and druids in Warcraft can manipulate the air; shamans call upon it for a wide and assorted range of powers, while druids prefer to summon hurricanes and tornadoes to destroy and incapacitate their enemies.
Skywall, one of the elemental planes, is home the Al'akir the Windlord and his minions.
Crono gets a "Wind Slash" attack in Chrono Trigger, which has the same Light (Heaven) element as his spells.
Also, Ventus, as his name suggests. Like Terra and Aqua, he can use the other elements in his regular spells as well, but only he can use the high level Tornado spell, and several of his finishing attacks mix in wind.
The MapleStory Knight of Cygnus Windbreaker class is composed of archers that use the power of the wind. One of their skills involves use of a magical wind that makes them immune to physical attacks, and wind-based attacks used in this state have their attack power increased. A different skill turns all neutral attacks into wind-based attacks, including their More Dakka and Rain of Arrows. They are generally more Glass Cannons rather than Fragile Speedsters, as they are quite slow and have low health compared to the other Knights of Cygnus.
City of Heroes has the "storm summoning" powerset, allowing a PC to attack with windgusts, hurricanes, and tornadoes, along with other kinds of storms. Oddly enough, the powerset also has a basic healing power associated with it.
There's also a recurring Aero or Tornado spell that occasionally shows up.
The protagonists of Final Fantasy V are each designated various elements, with the hero Bartz getting wind. As the Gladiator class in the remake, he can sometimes execute a wind-elemental attack dealing 9999 damage.
Kushala Daora from Freedom United and Frontier 2. It's known as the elder dragon of wind, and with good reason. It can generate a wind barrier around itself which will knock hunters off their feet if they get too close, which can complicate things for melee hunters. It has a breath weapon befitting its nature. Instead of fire or lightning, it fires blasts of concentrated hurricane-force winds, capable of doing heavy damage and throwing a hunter 10~15 feet into the air.
Nibelsnarf and Sand Barioth can shoot powerful gusts of wind in Portable 3rd and Ultimate. The former does it in a way similar to Gobul (expelling a vortex of wind from its mouth), which would have this power as well except it can only do it underwater. The latter can lay a vertical cyclone and then use it to spin and quickly charge at the hunter.
In Heretic, the Iron Lich boss has a windstorm attack that throws you up in the air and does damage until you escape.
Tornado Kirby and Wing Kirby from the Kirby series.
Sindel's scream fatality and Fujin's wind-skinner fatality in the Mortal Kombat series.
The game Lost Winds gives you the ability to control, move, and attack with - you guessed it - wind!
The titular monster hunters in The Witcher have a variety of simple spells ranging from traps that damage and immobilize anything walking over them, to blasts of fire, to limited mind control. Their most often used is a quick blast of wind that can push back, stun, knockdown, and disarm anyone in front of them at the time.
This is one of many elemental abilities Luigi of the Super Mario Bros. series has shown, while playing baseball or soccer. Being Luigi, the Wind is Green, and even gains a vacuum in Luigi's Mansion that can blow wind, fire, water and ice.
KOEI gives us the Dynasty Warriors, where wind is not a standard element but is generally common as part of attacks used as juggling or crowd clearing moves. Pang Tong is the most notable practitioner, possessed of powerful crowd clearing tornadoes as part of his moveset and his musou attack. His faction color and his attacks are, of course, green.
It appears with greater regularity in the Samurai Warriors series, where the available elements include ice, fire, lightning, demon, and, as per this trope, wind. A wind element attack Ignores Defense and damages enemies even if they block. No one character explicitly specializes in the element, but Shingen Takeda can easily call on it due to his moveset reflecting his motto Fu Rin Ka Zan. Several 'final' weapons also feature the Wind element, most notably that of Nobunaga Oda.
The Windmaster in Acrobat is a villainous version of this.
Homestuck's John Egbert is the Heir of Breath and, as such, is associated with and wields power over wind, but he is more of a Jack-of-All-Stats than a Fragile Speedster. When he first shows at least some control, he generates a massive cyclone that blows out the fire covering almost an entire planet.
In Pacificators, we know of three people with the power of air: Taffe,Enlil, and Gincoi (at least, Taffethinksso). Taffe is a rank B Pacificator, and Gincoi was classified as type 2 (weakest being 1). Enlil was classified at type 8 (strongest being 10). Enlil is so powerful at her control over the wind, she's capable of using a kite to fly upon the wind.
Zoophobia's Horris has powers of wind that he makes sure to boast greatly about to everyone within earshot, although he's yet to be soon actually using these abilities.
Alita's powers in Nexus seem to be based on flight and controlling air.
Winter of the Whateley Universe. Also, Stormwolf, who is anything but a Fragile Speedster.
Rayte in Trinton Chronicles had the ability to manipulate air in the form of green energy bands. He also could create sonic-booms, vacuums, and use pressured wind to cut into foes and objects alike.
Celestina Barbieri from Fate Nuovo Guerra specializes in wind and its sub-element, lightning. In particular, she uses it to increase her fighting efficiency by coating her sword in Razor Wind.
From the Global Guardians PBEM Universe, there's Twister, Thunderstorm, Summer Storm, Summer Cloud, Archdruid, Cloud Dragon, Shu, Teja Vayu ("Swift Wind" in Hindi), Dust Devil, Gale, Wind, Breeze (the hero, not the villain), Breeze (the villain, not the hero), Maelstrom, Flurry, Hurricane, Sirocco, Tornado, Vetra, Venta, Kamikaze, Dark Wind, and Turbo.
Despite them commonly being Fragile Speedsters, wind elements probably packs the biggest punch of all the characters in the show (literally and with regard to power).
Have you seen the Final Showdown? He knocks out all the bad guys by himself (who pretty much rule the alternate timeline) once, then completely takes them down while injured, using their own evil statues, all the while surrounded by a holy glow!
And before them, Jetfire and Landmine of Transformers Cybertron. Landmine's Cyber Tempest attack is especially powerful. He needs to use his Cyber Key to be able to do it. Jetfire just uses his jet turbines.
Twilight Sparkle uses a magical variant in Boast Busters.
Generation 1 has the Flutter Ponies and their "Utter Flutter." It takes a whole bunch of them (maybe all!) to do it, but it's pretty powerful, and magical, able to do more than simply physically blow stuff around, such as "blowing away" nasty magical effects when all else had failed. It's practically a Deus ex Machina.