As allways: artifacts and the most powerful enchanted items, books that boost your skills (gonna read them all, too), the best gems (flawless ruby and the sort,... oooh, shiny!) and any interesting objects left over from quests.
If the games has manequins, I'll collect a full set of every type of armor above the first two tiers (ussually iron, steel, fur and leater - not much point in those).

Cookbooks, assuming they will have them since there will be cooking in the game.....

In Morrowind my characters (usually Temple fanatics) always try to collect every of Vivec's sermons. Today I still haven't found all of them, but I keep on searching. And yes, I've read them all, although not ingame, but on The Imperial Library.

Oblivion ......... No.

So it depends whether Skyrim offers something interesting to collect.

I absolutely love to collect things of all shapes, sizes and rarities. In Oblivion, I loved to collected pewter and earthenware cutlery and kitchen goods because of their interesting appearances.

Weapons and armour are of course a given too, but I derive special joy in collecting as many books as possible - all types, no matter how common or rare or heavy or interesting, and I usually read them all too. The only pity I have is in the lack of a proper official bookplacing mechanism (hope this get's implemented this time!)

The absolute prizes of my collections were my copy of the Posting of the Hunt next to my incredibly rare and suggestive Daedric Lava Whiskey bliviongate:

Hell yes. Every weapon type, every book, every piece of armor, all clothing... EVERYTHING!

Dwemer Coins, Skulls, Skooma and other types of cool stuff that will be in the game.

bows and anything elven, books also!
i owned every book

I really hope they've copied the item manipulation mechanism from Amnesia/Penumbra for Skyrim, because the sloppy placing of items is what mostly limits my collecting urges. That and the way things resettle when you load a cell.

Barring those concerns, I'll likely at least collect all the books and a nice sword collection. Maybe gems.

Relics of Easter eggs, mostly. They're a great thing to collect

I will be collecting plants and herbs :turtle:

I like to collect staffs or short swords in oblivion ( they seem to be uncommon).

The Oblivon bridge-troll's note... Loved that crumpled scrap of paper more than Jauffre

I'm going to say it until serious attention is brought to it:

Big. Fat. Roiling. Piles. OF COINSSSSSSSS!

And precious stones, armor, clothes, books, ingredients, things like that. I also collect weapons (because you can never have enough weapons or ammo for them); anything that can cut, stab, bludgeon, disable, or otherwise deal grievous physical harm to another body or persons is thus acceptable.

... Coins. *rolls around on hoard*

In Morrowind, I mostly collected unique or hard to find books. In Oblivion I generally tried to get full sets of all the armor and weapons in the game (since that becomes difficult later on), and for some reason cheese. I went mad with trying to collect cheese. Probably a result of all the Shivering Isles I played.

Forks... It will be a lot of fun every fork I see, I shall conquer and claim as my own!

In Oblivion I collected everything. Literally, everything. It reaches a point where you have so much money that there's no point in selling loot anymore, so instead I have an impossibly overstocked Skingrad house (except for the bones and skulls, I put all of those in Benirus Manor)

in oblivion I collected all the different helmets ands all the daggers.
I probably chose daggers because they had the spirit of the short sword and long sword, but were smaller and easier to place

I also had a bunch of gems (luminescent and other wise) in multiple bowls

lastly, I collected every weapon with a unique model.
Umbra and that blue glass short sword come to mind

Icollected all of the types of swords and then all of the unique swords.

Books,Bows,Swords,Armor,Clothes and some Ayleid Crystals and anything else Ayleid

I will collect the souls of my enemies. bliviongate:

No idea. Ill see when I play.

Though I would like to see artifacts, like the Aylied statues in OB.

If I can collect the skulls of my fallen enemies then I will. Blood for the Blood god!!! Skulls for the Skull Throne.

I collect the usual things, Dwemer artifacts, Ayleid artifacts, and books.

Some of my characters have other interests, I collected people with one of my characters in Morrowind... I hope they bring back the "Lock" spell effect so I can make a wizard with a proper dungeon...

Edit* I remember one of my friends had a character named The Pants Bandit. He was a plague upon Vvardenfell, sneaking into peoples homes and stealing all of their pants.

I will collect all types of clothing and armour to wear

And of course all unique items.

I am a massive scavenger and collector. I always try to collect at least one of every item in the game, then I hoard anything with zero weight or anything that looks cool or is unique. I had about 6-8 houses in Morrowind set up as Museums of awesomeness.