Quests were originally a type of thread that involves a drawfag essentially DM'ing for the entirety of /tg/. There is an iconic main character that /tg/ shouts commands at, and the drawfag decides which action would make most sense for the character. The end result is a highly interactive game akin to free-form roleplaying, Choose Your Own Adventure books, and Point and Click computer games. Lately, almost no quests have drawfaggotry provided by the actual person running the quest (Questgiver). That, however, has freed writefags who can't draw up to run quests of their own.
Every quest goes on sup/tg/ with the tag 'Collective Game,' and so can easily be found here.
After quests were declared to be completely in line with /tg/, some people decided to leave and found an independent quest board called /tg/chan, but the average quality of quests there is...dangerously low.
The MS Paint Adventures forums] also hosts a number of quest threads. Some of them (including the main site's current comic, Homestuck) however are self-admitted railroads.
 Extended Quests
Drew the Lich was the very first of these threads, when Drew asked /tg/ for help getting adventurers to actually attack his tower. However, while it doesn't take long before Drew the Lich is less about us helping Drew so much as it is a story about Drew, it is still the very first Quest.
The Drew threads can be found here.
Ruby Quest is a tale of mindfuckery, panic, escape, and horror, as told by Weaver. The main character is a bunny girl named Ruby, who wakes up with no memories whatsoever of her past. The threads can be found here.
Dorf Quest is a tale of manliness, beardliness, rage, and dorf vs elf racial tension, as told by Gnome. The main characters are a Dorf named Beardbeard and a Rogue named Aldwin. The threads can be found here.
By all appearances, there will be more characters as time goes on. Beardbeard seems to have recruited an untrustworthy elf for an ally, while the incompetent Aldwin the Rogue is getting much-needed aid from a small girl named Lily and has found a love interest in someone who may very well be.
The Aldwin half of the story seems to have more thought put into it than the Beardbeard half, as well as an almost-plot line.
Joan's Joyless Journey is a quest revolving around Joan, a little girl whose life has literally gone to hell, as told by Sir Double Faggot. She hit puberty out of nowhere and has done a ton of stupid stuff such as punching a wall and attempting to use a dead headcrab as a hat. Also, Sergals.
The threads can be found here.
 Driblis Quest
Driblis Quest has no main article.
A quest following the antics of a kobold hatforger. The first successful quest to implement actual mechanics (discounting Dorf Quest's half-assed character sheets). May or may not be continued.
The threads can be found here.
 Iron Quest
A quest following the antics of a self-aware vonNeumann machine, a robotic overlord in control of dozens, nay, thousands of drones. Entirely too much time is wasted arguing about what to do with the local humans.
 Khorne Quest
A quest following the antics of an illiterate Khorne Berserker with limited vocabulary, insane strength and superb(or even supernatural) physical abilities. So far, has bashed through multiple walls(oh yeah), parry powerfist using face, got a note read for him, doing an assault jump(strike from the skies brothers!), kidnap guardsman, steal commissar hat and lots of BLOOD FOR THE BLOOD GOD/KILL MAIM BURN. Made by a drawfag named Khorga. Currently at part 3.
 Lost Future Quest
/tg/ selects a robot model (a Clarke engineering unit), which wakes up in the post-apocalypse and wanders around mexico, fixing everything he can and Bending the rest into submission. Despite these simple goals, Clarke 08 quickly becomes embroiled in the three-way war between humanity, the Skynet-esque Network, and the rag-tag Free Machines. Based on the Inn0cence: Lost Future setting, OP uses modified nWoD rules and writes a LOT of flavor text. The threads can be found here
 TG Meta Quest
This is a massive crossover quest. You are Task Force 38 of the Transpace Guard, and you blaze a path of fury across a corner of the multiverse, fighting Mary Sues and correcting dimensional shenanigans. A quest of strategies, tactics, epic clashes, and the nature of the multiverse. The quest for two years, going past the Mayan Apocalypse and ending in early 2013.
Threads are here
A quest following the antics of an anonymous by the name of David Lister, a Giant Robot pilot for the Principality of Zeon, the nominal bad guys in Japanese shades of grey mecha war anime Mobile Suit Gundam.
Some trolls have called for it to go to /m/, under some bizarre pretext that Roleplaying is no longer a /tg/ purview and that longtime namefag questrunner I apologised on 4chan wouldn't just get told to take it right back to /tg/. Even stranger is their claim that he should be going about killing everyone in the misguided belief that this would somehow make it more enjoyable.
In anycase, the threads are all found here
 Zerg Quest
This Quest began with the Starcraft Overmind creating Cerebrate Anon to think outside the box. The questrunner has since taken up namefagging under that name. Fans have named its brood the Hashashin Brood, though Cerebrate Anon never seems to get around to calling it that. The quest has gone from tedious Starcraft sim to horrible rape sim to empire-building wargame and beyond (and back to rape sim, some weeks), with perennial nemesis Kingston, a CREEEEDlike character that outsmarts all of /tg/ about once per week.
The quest generally ran every week,
Wednesday at about 21:00 servertime whatever day Cerebrate Anon has free this week. Threads 4 and beyond are available here (with threads 1 - 3 archived, but potluck for tags): http://suptg.thisisnotatrueending.com/archive.html?tags=Zerg%20Quest
Zerg Quest ran for 2.5 years, and Cerebrate Anon loves you all.
 One-Shot Quests
 Knight Quest
Knight Quest has no main article.
Knight Quest is the tale of an incompetent knight trying to save the princess from the Evil Villain. Characterized by absurdist humor and, well, more absurdist humor. The thread can be found here.
Blockhead has no main article.
Blockhead is pretty similar to KnightQuest in that it is random and frivolous. Made initially as a parody of both the 'RAILROADING' trolling and as a fun thing to kill time with, it quickly became the collaborative effort of many different drawfags. An amusing adventure. The thread can be found here.
Click title for the subsection of the Ruby Quest article this got shoved in to.
A ridiculous side story told by Weaver about Tom's twin brother John. A must-read. The thread can be found here.
 Grue Quest
Although spammed up the ass by a soulless troll, this quest shows real promise. /tg/ is a grue. It can kill. It found a dead Nazi. It has a grenade.
Watch out for trains.
Thread can be found here.
RangerQuest has no main article.
The first thread didn't even get archived, guys. What the heck. And the two that were don't have tags.
 Hamburglar Quest
Hamburglar Quest has no main article.
A quest in which the hero is a goddamn hamburglar trapped in a room filled with skeletons. And feces. And 50 feet of dental floss. The thread can be found here.
 Oneshot Quests Gallery
 The New Quests
 2012: The Summer of Questfags
2012 saw a sudden explosion of quest threads as mods everywhere declared them /tg/-related material. This drove several budding quests from across the 4chan to /tg/, where fags raged about Warhammer and MTG threads being replaced by the likes of Katawa Shoujo Quest and Battletech Quest. Attempts to create a /q/uest board were thwarted when /q/ was revealed to be a board for meta and talking to mods, and quests were deemed /tg/-related.
This new generation of quest threads was characterized by writefags and DMs who were tired of meeting IRL. Instead of drawfags drawing events and actions, questfags would select from a series of choices presented to them and the OPs would then post the written results, usually with a related picture they had grabbed from somewhere.
Many quests of 2012 disappeared with the end of Summer, leaving only a small portion of popular survivors to see the dawn of the Mayan Apocalypse.
 The Quests of 2013
Hormissar Gaunt, the hormagaunt comissar
 QuestQuest Gallery
QuestQuest is a series of pictures that basically consist of the Quest characters being shoved into the other Quests.