Finish your drink and Head Desk if an ally is AFK for the entire match. Feel free to drink some more if he reconnects much later and dies over and over trying to engage level 12+ enemies when he's level one.
Take a shot every time you accidentally Kill Steal.
Take another if you're a support or tank and a carry really needed it.
Take two if the person yells at you for it and doesn't believe it was accidental.
Take a drink and Face Palm when someone on your team tries to imitate a famous player's crazy playstyle or unconventional build and fails miserably at it.
Take a shot whenever you try to help a team mate get a jungle buff and end up stealing it instead.
Chug your drink whenever your champion is channelling an ability for more than one second. If you're feeling hardcore, do this for recalls as well.
Take a drink for each time you pull off a daring escape when your team gave up on you.
Two if it's unconventional (eg. Quinn's backflip, enemy knockback sends you to safety, Baron or Vilemaw disables your pursuers...)
Finish your drink if you manage to just walk out without using your abilities.
Take a drink whenever you land a blind skillshot (into the fog of war) to score or secure a kill.
Two if it's at max range.
Three if it's global, or extremely long range (like a Lux, Ashe or Jinx ultimate).
Finish your glass whenever a knockback or movement effect causes you to land a gap-closer or pull (such as Amumu's bandages or Blitzcrank's hook) from BEYOND its max range.
Downgrade this to just a single drink if a Thresh is on your team and you used his lantern, otherwise liver failure is guaranteed.
Take a drink for each crowd control in an unbroken chain. Examples include juggling with knockup without letting your opponent touch the ground, or chaining stuns so the opponent gets no control in between the abilities connecting.
Take a sip for every count of any variation of "throw" or "feed" in chat.
Take a sip for every count of "noob team" or a premature "gg".
Down the bottle if it's a support, especially a Soraka saying it.
Finish your drink if it's the complainer who's failing and/or throwing the game.
Drink whenever someone goes really in-character as their champion in the chat. Drink again if someone yells at them to stop being an idiot.
Take a long drink and sigh if you realise that your team could be doing much better than they are if people used chat or smart pings to communicate.
Take another (the drink and the sigh) if you're trying to encourage chat conversation and discussion and no-one else is bothering.
Drink if your entire team is in alternate skins.
Chug if everyone is in Legendary or Ultimate skins so that no-one has their normal voice pack.
Chug if you get a full set of skins in your team (eg. the five members of Pentakill, a full set of Pool Party skins, the three Heartseekers etc.).
Drink when someone starts a surrender vote.
Another if it's started by the person with the worst kill/death ratio on the team.
Take a shot when a lane demands to be ganked with unwarranted rudeness. Take two if you actually do help them out and they don't go in with you. Take an extra shot for every time you ping indicating you're about to gank.
As Alistar, take a drink of shame every time you knock back an enemy with Headbutt in a position that is actually favorable for them. Take a drink of triumph for every Headbutt canceled into Pulverize that you pull off.
As Pantheon, chug triumphantly should you manage to damage at least one enemy champion with Grand Skyfall. Chug twice should you kill at least one enemy this way!
As Janna, take a drink of shame every time your Monsoon doesn't work as you hoped. Do this as well if you continue to channel Monsoon and get yourself killed for it.
As Blitzcrank, finish your glass for every time you pulled an enemy champion from the fog of war with Rocket Grab.
Down a shot if you accidentally kill your opponent with your Rocket Grab. Two if someone calls you out on it.
As Sona, take a shot for every Power Chord you apply onto a champion. Take a sip instead if you don't feel like having your stomach pumped afterwards.
As Ryze, take a sip for every time your passive makes Overload immediately available to you again (pretty likely to kill you if the match lasts at least 30 minutes).
As Cassiopeia, take a sip for every time Twin Fang gets its cooldown refreshed from hitting a poisoned champion (pretty likely to kill you if you can somehow still aim enough to poison champions while drunk).
As Skarner, please do not take a sip every time you use Crystal Slash. It will definitely kill you.
Or doing this as Karthus every time you use Lay Waste.
Making use of a drinking hat!... which apparently is attached to a few kegs.
As Swain, drown your sorrows if your Mana Meterruns out at the most inconvenient moment and everyone gangs up on and kills your defenseless human form. Also applies to Anivia if you were counting on Glacial Storm acting as a no-man's-land between your and their team and you all get jumped the moment it stops casting.
Hardcore mode: After a full teamfight, chug for each second you spent with your ultimate active.
As Anivia, take a drink every time you miss a QE or RE combo.
If you get egged, start chugging right from the bottle until you resurrect. Finish the bottle while laughing if there were enemies nearby who failed to finish you off.
As Ahri, take a sip for each Charm you land.
As Malzahar, take a shot for every champion killed in a row with a single Malefic Visions.
Finish your glass every time your ultimate is interrupted by someone, and drown your bottle if this ends up killing you.
As Mordekaiser, drink each time your ultimate gets you a champion's ghost.
Drink again for each kill or objective this ghost secures you.
Finish your drink, start another and finish it, then start another if you score a Pentakill with a carry's ghost.
As Leblanc, take a drink every time you successfully juke an opponent, and finish your glass if you fail and get killed.
As Zilean, chug a glass every-time you ult a champion who's near death, but then proceeds to try and escape, but only manages to die after your ult as worn off, wasting it. Chug another if this proceeds to get you and any of your other allies killed.
As Karthus, take a drink whenever you kill a champion from across the map with Requiem after they fled from whichever of your teammates' they'd been fighting. Down your glass if you manage to kill them right after they Recall.
Alternatively, take another sip if your teammate yells at you for a Kill Steal.
As Soraka, take a drink when your Wish skill saves an ally that's about to be killed halfway across the map. Take another if this boost of health allows them to kill whoever it is they're fighting.
Prior to her rework, another challenge was to take a drink whenever you got yelled at for "giving Mana to the enemy". (Soraka's old kit included a move called Infuse that would either give MP to an ally or silence an enemy, but the animation on either effect is the same, making it look like Soraka was giving mana to enemies.)
Going along with the above, take a sip as Cho'Gath or Nasus if the sheer size of the aforementioned champs prevents the enemy from targeting a squishier ally who's hiding in your shadow. Take a shot if you're intentionally pulling off this strategy.
Chug during the duration of your Magical Journey while trying to flee the enemy team. Celebrate and finish the drink, if the enemy took a Magical Journey with you, to their doom at the hands of your waiting teammates at the end.
Take a sip everytime your Bard fails to do their job at supporting the team (Missed stuns, locking down his own team to be killed with Tempered Fate, leading the enemy team to yours when you aren't ready for a team fight with Magical Journey.) Down the bottle(s) if it becomes apparent that your team's Bard is doing this intentionally to troll your team, and file a report for Griefing: Assisting the Enemy team post-match lost.
As Tahm Kench, take a drink every time you successfully use your W on an enemy.
Finish the glass if you fail to because they only have two stacks on them.
As Vel'koz, take a sip every time you manage to (purposefully) nail someone with the split shot from Plasma Fission. Finish your glass if the initial shot and the two split shots hit their intended target.
As Fiora, take a sip every time you parry an attack. Down the whole glass if it's an Ultimate !