A couple examples of my all time favourite types:
 
Wow  
The Barrens  
Collect 60 bone remains from Quelboars.... cheers. 
 
Neally every zone
Kill x Murlocs... cheers 
 
Eve
Kill wave after wave of Serpentis ships.... (3 hours later) cheers 
  
Would you mind mining me some Veldspar please, oh you don't have a hauler well, sorry dude I need it.... cheers 
 
Travel to Station x, pick up these items... oh your cargo isn't big enough hey, well it's okay you can take the trip multiple times...  it's only 12 jumps

Anything with a droprate that isn't 100%. 
 
 
I'd rather have a killcount quest for killing 20 dudes than have a shitty quest to collect 8 claws, where the claw droprate is less than half.

The priest quest in WoW where you had to kill stags in Aszhara, to get three items with like 0.1% drop rate. Took ages!

Escort quests with a AI companion that walks faster than your walking speed, but slower than your running speed.  
I'm looking at you, World of Warcraft.

It's pre-Cataclysm so I'm not sure if they've changed them but anything with Nesingwary; employing WoW players to commit eco-genocide since 2004.

@PenguinDust said:

It's pre-Cataclysm so I'm not sure if they've changed them but anything with Nesingwary; employing WoW players to commit eco-genocide since 2004.

The ones in the TBC expansion where the worst,Blerg.

Group quests. I had a number of rl friends that played WoW when I did and everyone always did their own thing. Trying to get together a PUG for these group quests was often more difficult than soloing the quest yourself.

@PenguinDust: @Jaded_Racoon: Skinning is awesome.

Also, no one has mentioned Trial of the Sea Lion (Alliance) for WoW?

Any escort quest where the opposite faction can kill the quest npc.
 
AIShdoaihsoaingoaisnfdas.

escort quest, usually it requires some help from people because there are more mobs attacking. 
 
a drop rate that is less than 50%. i don't care to much about not getting it every kill but make sure there is a chance.
 
long quest lines.

Anything with a droprate that isn't 100%.   I'd rather have a killcount quest for killing 20 dudes than have a shitty quest to collect 8 claws, where the claw droprate is less than half.

Quests that make me fill up my inventory, for example having multiple quests in the same area that require you to carry some kind of equipment on you. Having one or two of thee at a time isn't bad but when your going around a quarter of a bag of things to use during quests it become annoying. (Note: not talking about gathering stuff I mean like getting a fire extinguisher to put out fires, do you really need to put it in my inventory can I just have a temporary ability or something.)

Anything with a droprate that isn't 100%.   I'd rather have a killcount quest for killing 20 dudes than have a shitty quest to collect 8 claws, where the claw droprate is less than half.

ESCORT

Most of EQ quests. Especially ones that required you to kill mobs that had spawn cycle of hours or days and it was random - maybe even add insult to injury by making it a raid mob, so whoever got their guild to the location and buffed fastest, got the mob.

Final Fantasy XI 
Level 50 level cap quest.
 
You needed 3 rare items and back when i was playing, it could have taken weeks or months before you got the items to drop (they were very low drop chance).   Also the monsters that dropped the items were surrounded by higher level stuff that it made it extremely difficult for a small party of level 50's to kill them efficiently.   I ended up doing this quest with like 18 other people and had to roll against many others for the item.  I eventually got lucky.   But man It was probably the most difficult and annoying quest i have ever done.

Final Fantasy XI 
 
The Magian Trials
 
Sub-Quest after Sub-Quest, fulfilling really increasingly absurd goals. For example Kill X number of Mobs with X Skill during X weather - The mob requirement was often in the hundreds, the weapon skills varied, if you had a weak one to use you were in trouble, and the weather.....was totally and 100% random. I spent over a week searching for a Lightning Storm when I was doing some of the Hand to Hand MTs. 
 
So fucking glad I don't mess with this game anymore...MMOs....headachey.

Quests in WoW where you had to collect things that had ridiculous drop rates. Like a 0.5% drop rate.

Escort quests in WoW were awful, especially because most of them have a very long walking introduction that you will have to sit through again if you die. I remember one quest in Desolace or something where you had to escort the slowest and most talkative turtle in the world all the way across the map.
 Also, quests that force you to go out to a place that you just went to or fight the same kind of enemy are pretty bad too.
I played a Paladin Tank in WoW, so kill quests were actually kind of fun, just because I would always try and see how many of the target I could round up and kill.

i thought WoW:BC's Nagrand zone

Kill 30 cows/birds/gazelle

Kill 30 more stronger cows/birds/gazelle

Kill 30 strongest cows/birds/gazelle

was the worst

Water totem, Call of Water, quest for Shamans. Vanilla and no mounts at your level. Go to the barrens, then to the other continent, then back to the barrens, then back to the other continent, then back to the barrens, then back, then back, back, and back back back back back back back back back back.

Water totem, Call of Water, quest for Shamans. Vanilla and no mounts at your level. Go to the barrens, then to the other continent, then back to the barrens, then back to the other continent, then back to the barrens, then back, then back, back, and back back back back back back back back back back.

Any escort quest in any MMO.

Collect an item from an enemy that should always drop from it, but doesn't. 
e.g. (this is a crazy example, not an actual quest). 
collect x snakeskin. 
collect x armour scraps 
etc.

The Positron TaskForce was so god dam terrible.

Low drop rates, escorts, those who you have to to something with the corpse of the mobs you kill(Example plant a flag on them, burn it etc), I always forgot to do it and ends up killing way more than necessary. And those kill quest where there isn't even enough mobs for you to complete the quest even when you have the whole zone for yourself. Waiting for your enemy to respawn makes sense doesn't it?

Defias Messenger in Westfall anyone?

i thought WoW:BC's Nagrand zone

Kill 30 cows/birds/gazelle

Kill 30 more stronger cows/birds/gazelle

Kill 30 strongest cows/birds/gazelle

was the worst

Defias Messenger in Westfall anyone?

I've only ever played a few hours of any MMO that actually has a questing system. None of them were terribly annoying, but some of the drop rates on items were. No need to go into specifics about the game, but it was a decent FTP.

I've only ever played a few hours of any MMO that actually has a questing system. None of them were terribly annoying, but some of the drop rates on items were. No need to go into specifics about the game, but it was a decent FTP.

@niamahai said:

i thought WoW:BC's Nagrand zone

Kill 30 cows/birds/gazelle

Kill 30 more stronger cows/birds/gazelle

Kill 30 strongest cows/birds/gazelle

was the worst

this

@Astras said:

@Example1013 said:

I've only ever played a few hours of any MMO that actually has a questing system. None of them were terribly annoying, but some of the drop rates on items were. No need to go into specifics about the game, but it was a decent FTP.

Then my friend, you have never really experienced the quest grind! Early quests are traditionally quick and easy, to ease you into the game.

Well, I'd say that my estimate was a bit low. It was a game with a level cap of 50, and I'd say I spent 20-30 hours on it. The quests never really got too grindy, though, as the numbers of items in fetch-quests were never huge. The only difficulty to most of the quests was that some of the mobs were difficult to kill and required grouping up with others to finish, and the random PKers who would sometimes run through and wipe you out. The game had true open-world PVP with just towns as PVP-free zones (where you had to challenge/accept duels to fight), and when there were PKers near the town entrances it was sometimes hard to just get out to go do quests, even though I was only in the first big zone after the beginning area.

I have no problem with the open-world PVP, and it's in fact why I was trying the game out. The real issue was that you had to be at or near the level cap to compete with the max-level PKers (along with a certain level of gear once at that level), and I never spent enough time to get there (and as I said, the process was hindered by max-level PKers).

The other MMO I played didn't have quests and was focused entirely on end-game PVP (which you could theoretically do as early as level 45 in a game with a level cap of 75) and city control/sieging. The lore was extremely deep, and the world was good-sized, but mobs only existed as a vehicle with which to reach max level and be more effective at PVP.

where the fuck is mankrik's wife?!

WoW - anything underwater

But my favorite was the damn attunement quests.  The Horde one for Onyxia was ridiculous.  Besides needing a raid to hop around the world killing dragons.  You had to go chase down Rexarr in Desolace more than once.  The series to get the Upper Blackrock Spire key was crazy long too.  Grind the dungeon many times where each of 4 fragmentsmight drop.  And roll against everyone else for them.  Then assemble it and go to Wetlands to another continent to kill a dragon (you get 3 chances and are boned if you waste them).    

Quests with low drop rates. Also quests that require you to be in a party or be over leveled for it.

WoW - Recon Essentials

I skipped that quest on everything but my first character. Spending over an hour+ trying to get that smithing tuyere to drop did horrible things to my blood pressure. Not to mention it only drops from one mob which happens to share spawns with two other mobs, so you may be forced to kill off all of those in hopes that the mob type you need will spawn in their place. Also, Searing Gorge is just an ugly, depressing zone.

@YoungFrey said:

But my favorite was the damn attunement quests.  The Horde one for Onyxia was ridiculous.  Besides needing a raid to hop around the world killing dragons.  You had to go chase down Rexarr in Desolace more than once.  The series to get the Upper Blackrock Spire key was crazy long too.  Grind the dungeon many times where each of 4 fragmentsmight drop.  And roll against everyone else for them.  Then assemble it and go to Wetlands to another continent to kill a dragon (you get 3 chances and are boned if you waste them).    

http://www.youtube.com/watch?v=vyQ-7o397Uk&feature=channel_video_title

My favorite quests are the ones where you are sent to collect things from things that should obviously drop them, yet they don't.
 
Collect 20 rat ears.... you kill them and you get one ear.. or none?... I mean wtf? Don't all rats have ears?

There was a quest in the Barrens where you had to kill centaurs until it finally spawned a Chief centaur and it would take about 50 kills before he spawned and if you weren't right next to where he spawns when he does, chances are someone else would swoop in and kill him.

"Hey i need an escort to get over the river, but im basiclly gonna walk in a long ass circle for 5+ minutes to see how many mobs i can pick up before i actually go any where near the other side of the river...".

Worst quests: Boring "collect/kill X creature" quests. 
I know it's a requirement of MMORPGs, but damn...they suck.