A full Karma skin gallery, plus the practical point: some skins change the silhouette enough to matter in a fight.
Before the cosmetics: Karma is a mage at 525 attack range whose job is to land a cooldown for a burst of damage, then be safe and largely useless until it returns.

Karma has 15 skins, excluding chromas. The art below is the in-client splash.
Skins change no numbers. They are not therefore free of consequence — a skin that alters the silhouette or recolours an ability changes how quickly an opponent reads what you just cast.
That cuts both ways, and it is the honest reason some players keep the base skin on champions they take seriously.
Karma's damaging abilities will reduce the cooldown of Mantra.
Karma sends forth a ball of spirit energy that explodes and deals damage upon hitting an enemy unit. Mantra Bonus: In addition to the explosion, Mantra increases the destructive power of her Inner Flame, creating a cataclysm which deals damage after a short delay.
Karma creates a tether between herself and a targeted enemy, dealing damage and revealing them. If the tether is not broken, the enemy will be rooted and damaged again. Mantra Bonus: Karma strengthens the link, healing herself and extending the root duration.
Karma summons a protective shield that absorbs incoming damage and increases the Move Speed of the protected ally. Mantra Bonus: Energy radiates out from her target, strengthening the initial shield and applying Inspire to nearby allied champions.
Karma empowers her next ability to do an additional effect. Mantra is available at level 1 and does not require a skill point.
No mortal exemplifies the spiritual traditions of Ionia more than Karma. She is the living embodiment of an ancient soul reincarnated countless times, carrying all her accumulated memories into each new life, and blessed with power that few can comprehend. She has done her best to guide her people in recent times of crisis, though she knows that peace and harmony may come only at a considerable cost—both to her, and to the land she holds most dear.
Skins are tied to the account, not to you. Anything bought on a smurf stays on the smurf — worth knowing before spending real money on one.
Full Karma page — abilities, stats and every skin →