Double post because patch 4.13 is out. It's pretty much all balance changes like the last few have been (for the most part). For those of you too lazy to look at the site, this is what happened.
Skins
These skins will be available for 750 RP each:
Debonair Ezreal and Vi
Headhunter Caitlyn
Skins - Splash Art Updates
The following skins got their splashes replaced with the Chinese ones:
Champions - Reworks
Sona is the only one this time. Her model got some touch ups to go with it.
Champions - General
Braum nerfed...again. Passive damage and Stand Behind Me nerfed AGAIN, and his ult takes a hit this time as well.
Elise's Cocoon width is narrower. Also Rappel range got nerfed.
Eve's Hate Spike base damage got nerfed, but increases in ratios + decreases in mana cost.
Gnar is not in this patch.
Gragas nerfed. Barrel Roll does reduced damage to minions, and Drunken Rage now costs mana.
Graves's Buckshot and Collateral Damage got damage buffs (in Buckshot's case, changes to the damage reduction of subsequent hits with one cast).
Hecarim's passive now scales with level, and Rampage (helihorse) costs less mana.
Janna's Tailwind aura has a larger range, and Howling Gale's cooldown is started as it's cast (as opposed to released).
Jinx gets excited when an inhibitor goes down.
Kayle's nerfs from 4.11 were tuned back a bit.
Kog'Maw got a base HP nerf (in exchange, an HP/level buff), and the Caustic Spittle shreds less at earlier ranks.
LeBlanc's Distortion costs less mana at higher ranks.
Lee Sin's Cripple no longer reduces Attack Speed, and his Safeguard shield doesn't last as long. In return, he got a Health Regen Buff. I'd expect further Lee nerfs in later patches.
Lissandra got more DPS (and slow on her ult) in exchange for some power on her Ring of Frost.
Lucian's Relentless Pursuit has a higher cooldown and no longer removes slows.
Lulu's Glitterlance slow no longer scales with AP, and her Whimsy's movement speed buff has been shortened at earlier levels in exchange for a reduced mana cost at higher ranks.
Lux buff hype! Her passive now scales with AP as well as level.
Nami's Movement Speed was nerfed as well as her Ebb and Flow cooldown.
Olaf buffs helped out his Undertow, Vicious Strikes and his ult Ragnarok.
SHEN'S ULT BUG HAS FINALLY BEEN VANQUISHED ONCE AND FOR ALL. PRAISE LORD LTRANDOLPH.
Sivir's ult got increase in the initial movement speed buff duration at later ranks. The total duration remains the same.
Thresh's Flay now shields only one allied champion, and his ult now only damages upon the first wall being broken.
Tristana was...nerfed? Neither the Rocket Jump slow nerf or Explosive Shot damage nerf don't do too much to AD Tristana (AP, maybe).
Varus's ult now has a lower cooldown, especially at higher levels.
Vayne was buffed by way of Attack Speed and AD boost from Final Hour per Doj's link.
Yasuo's passive shield is slightly shorter, Steel Tempest scales less with attack speed, and Wind Wall no longer gives bonus flow to Sweeping Blade. Nerfs all around.
Ziggs's ult is now 120 second cooldown at all ranks.
Zilean's Time Bomb explosion no longer ignores spell shields (the application of the bomb did, now the application ignores them).
Champions - Insignificant Stuff
The following champs received minor/bug fixes:
Gragas
Jax
Sona
Shyvana
Thresh
Vayne
Vel'Koz
Yasuo
Items
Banshee's Veil cooldown increased. Burst magesc rejoice!
This is a WIP. In the meantime go read the notes, you lazy bums.
http://na.leagueoflegends.com/en/news/game-updates/patch/patch-413-notes