Going to update this thread with quests I've "stumbled upon" as I play.
TELDRASSIL

As you quest in Teldrassil (north-east part of it, level 10-12 area) and most probably gathering those mossy tumors off timberlings, there is one rare level 13 timberling - Blackmoss the Fetid who drops Moss-twined Heart which begins a quest 'The Moss-twined Heart' You can find him roaming around the lake and is rather easy to deal with at level 11+ (I usually find my characters quest there around this level) The reward is sweet - a timberling that will fight on your side for 20(!) minutes or until killed.
There are also two big plants - to north-east and north-west from Dolanaar (to the far left and to the far right as you exit Darnassus towards Dolanaar) that give you 1 quest each.
At the area where you do Tears of the Moon (given at Darnassus, Temple of the Moon) there is a druid-like cat named Mist. She is lost and you get the quest to lead her out of danger to her master (sentinel standing near the Moonwell), Mist is very easy to miss because even if you gather belts off herpys for the quest given by the same sentinel, you are likely to avoid that area as harpys there are 1-2 levels higher and the caster types are pretty dangerous if you are level 9-10. I'd say you'd have to walk straight north-west from the Moonwell and lean to whare Teldrassil actually ends (call it a bark - I used to think it was mountains hugging Teldrassil until I finally realized Teldrassil is actually a tree^^)
Imortant note! There is one quest that is not availible to you until you train cooking. So don't be a dwarf and spend a few coins on it and you get 250 to your Darnassus reutation plus a tasty sder kabob. The quest giver (cooking trainer) is named Zarrin.
I guess it is all there is to say about Teldrassil.
DARKSHORE

Beached Sea Turtle and Beached Sea Creature are objects you will meet along the way while questing in this area. All of these quests are handed in to the same quest giver in Auberdine.
Not many people read into 'WANTED! Murkdeep!' quest description and so not everyone is aware that to summon Murkdeep you have to keep killing murlocs at the area he spawns.
Also the Twilight Thugs and Twilight Disciples are rumored to drop Book: The Powers Below that I still haven't had a luck to get. It begins quest The Powers Below. You can find them surrounding a small lake in the south of Darkshore (and to the right from the road heading to Astnaar). South of that lake is The Absent Minded Prospector.
To the north (the most northern part of Darkshore) you can get two quests from a gnome named Gelkak Gyromast.
AZUREMYST ISLE

Nothing much to say about this area except that this area is famous for Blood Elf Bandit Mask that sometimes drops from Blood Elf Bandit stealthing in northern part of the Isle. He also drops Blood Elf Communication thats starts a quest.
Once you enter Azuremyst from the boat you will likely see an infected nightstalker runt. Kill it. it will drop a Faintly Glowing Crystal to make you busy (quest Strange Findings).
If you are a reputation or Lore-Master title hunter you would want to drop by a starting draenei area Ammen Vale (eastern part of the Isle) and quickly do the quests there. When you get to the blood elves around there (north-west of Ammen Vale) - and you'll be needing Surveyor Candress to be slain for a quest - don't forget to loot his corpse (as the quest only requires you to kill him, not get any items off him) and you will obtain Blood Elf Plans which is a quest starter.
Back to northern parts of Azuremyst Isle, you will be given quests by furbolgs (supposedly you have already done the quest that teaches you their language) and one of those quests will require you to get to the coast (Murlocs... Why here? Why now?) for stillpine grain which can be either objects (looking like sacks of grain all around the area) or a drop off murlocs, When you are at that place, scout the coast for a bigger gray murloc named Murgurgula (a very suitable name for a murloc) and leave noone alive - he drops Gurf's Dignity which Gurf the furbolg at Stillpine Hold will much appreciate to have back!
I think the last item to mention is a Rune-Covered Tablet looted from the naga to the south. Numbers vary, but it is around 2.5, 3% droprate and you might finally give up on getting it though.
BLOODMYST ISLE

At Bloodmyst Isle everything is pretty much easy to find/discover. Only two drop items that begin quests are Red Crystal Pendant which drops off the murloc Cruelfin [Rawgrlgrlgrlgrlgrrgle] thats spawns at the southern coast of Bloodmyst Isle (starts quest 'Cruelfin's Necklace') and Tzerak's Armor Plate that dropps off a demon named Tzerak to the south-west from the Blood Watch (starts quest 'Signs of the Legion')
There is also this quest giver I have almost missed on my way to do a 'The Missing Expedition' quest. It's Researcher Cornelius and he gives you quest 'They're Alive! Maybe...' He is located to the north-east to the entrance to the path up the mountain (where you kill Zatakh - the big spider) and if you take the quest he offers you can do it together with 'The Missing Expedition'
DUN MOROGH

So long as I remember (and I haven't found any info on the internet that would disapprove that) there is no drop items that begin a quest in this area.
Of all the objects i can think of there is only one - A Dwarven Corpse - that is easy to miss (it starts 'A Pilot's Revenge'). However, if you have previously completed 'The Lost Pilot' quest, you will have no issues finding the corpse as the quest gives rather detailed directions as to where it might be (A Dwarven Corpse lies on the left side from the path to North gate, across from the quest giver.)
Speaking of Dun Morogh, I decided that I put a small note on Gnomeregan Exiles in it as well. I personally had a hard time doing 'Data Rescue' quest so this information could help those who might need it.

Here is the map. You start your way in a non-instance zone of Gnomeregan and it is there that you obtain the white punch card you need - it drops off non-elite gnomes running about the area.
When you have the white card, get down on the elevator, do not enter instance yet! Go to Techbot area (choose right side when you reach the fork). There are several Matrix Punchograph 3005-A objects. Use any of them and get your yellow card.
Now it is time to enter the instance. Go back to the fork and choose left this time.
Punchograph 3005-B is located in the bottom of the Dormitories. Use it and get your blue punch card.
Now off to Matrix Punchograph 3005-C. You'll find it on a platform in Launch Bay (right in the middle of the room) and it is guarded by Electrocutioner 6000. I think you have to fight him as he is positioned very close to punchograph. Get your red punch card and proceed to the Matrix Punchograph 3005-D.
Matrix Punchograph 3005-D is located at the very bottom of the Engineering Lab. Using it will reward you with Prismatic Punch Card.
You can leave through the back entrance now supposedly you've dealed with Electrocutioner 6000 and he dropped Workshop Key for you that opens the back gate.
LOCH MODAN

Farstrider Lodge for me was area I discovered many characters after I rolled my main one so just a map for you to remember there are actually two flight paths in Loch Modan =)
Also an interesting quest chain awaits you at the Dam to the north.
As for quest giving objects that are not involved with any other quests and thus hard to find - I am not aware of their existance in Loch Modan.
Almost forgot!
ELWYN FOREST

Normally I try to avoid Northshire and Goldshire as often as possible but it may be less annoying to quest there on other realms.
Also, apart from Gold Pickup Schedule, that drops off mobs around Hogger area and Westfall Deed - off defias bandits, there is hardly anything worth mention in terms of searching.