Currently Airing Anime

Sword Art Online Ep 10 - For those who think that Kirito seems a lot less overpowered in this episode, keep that red-tinted moment in his fight against Heathcliff in mind; it becomes a plot point later on.

Anyway, Sword Skills shown so far:

 Spoiler

One-Handed Sword

Horizontal - Single horizontal slash.
Vertical - Single vertical slash.
Slant - Single diagonal slash.
Vertical Arc - 2-hit combo of consecutive slashes in a V-shape.
Horizontal Square - 4-hit combo of consecutive slashes in the shape of a square.
Sonic Leap - The user is propelled high above the enemy, slashing as he lands.
Rage Spike - The user charges toward the enemy to unleash a single, powerful slash. Can cover long distances.

Dual Swords

Starburst Stream - 16-hit combo of consecutive slashes.

Rapier

Linear - A single forward thrust.
Star Splash - 8-hit combo of consecutive thrusts.

Two-Handed Sword

Avalanche - Supposedly an extremely powerful blow that can cause the target to stagger even if guarded, but Cradil never gets to use it; he gets interrupted by Kirito's Rage Spike.

Curved Sword

Reaver - Sort of like Rage Spike, except that the distance that can be covered isn't very long. Used by Klein in ep 1.
Fell Crescent - See Sonic Leap. Used by the Lizardman against Kirito in ep 8.

Katana

Note: The following skills were all used by Illfang the Kobold Lord in the Light Novel. Some may have been excluded in the anime, but I'm too lazy to check.

Tsumujiguruma - The user jumps into the air and lands spinning with Katana outstretched. Deals heavy damage to surrounding enemies and may stun them.
Ukifune - An upward slash that launches the target into the air. Chains into Hiougi; if successfully chained, there is no escape.
Hiougi - 3-hit combo consisting of an upward slash, followed by a downward slash, finishing off with a powerful thrust.
Tsujikaze - A single slash too fast for the eye to see.
Gengetsu - A series of upward and downward slashes.

Two-Handed Axe

Whirlwind - The user spins his Axe like a whirlwind to strike the enemy.

Martial Arts

Embracer - The user thrusts forward an open palm, fingers first, and embeds his hand deep inside the enemy's body.