What items are you obsessed with? Please, leave answers like weapons or clothing out of this, I'm talking about other items here.
I always liked those flushy teddy bears...

Gnome's. I collect garden Gnome's and I carry one around with me at all times. I also collect other weird items when i find them but to a lesser extent then
Garden Gnome's. Sometimes i will actuly go on "Gnome hunts" were i just wander places were I think Gnome's would be serching for them.

And to a lesser extent I also collect Pre-war money, so i can throw it around my base (or on my Gnome's) and act like a rich person.

Biggest Nuka-Cola freak out there. I got the Nuka-Chemist perk and I litter my place with Nuka-Cola Quantums and Victories.

Ammo.

Toys of all types. Dinos, rockets, cola-trucks, gnomes, bears, pool balls, cameras, cars...
And then I line them up on shelves.

I used to collect toys in real life before I was married. This might be repressed urges bubbling out.

scrap metal (lol)

Harmonicas

Wow...looks like a lot of psychosis here...

I collect anything that isn't nailed down(and a fair bit that is), but my all-time favorites have to be Doctor's Bags, Tin Cans, Power Fists, and Empty Nuka-Cola bottles. I have lots of those things just stacked all around The Sink.

-Nukeknockout

different animal hides, eggs, tails, and meat. i have it lying on shelves for display.... as my "trophies". :gun: :spotted owl:

Nuka cola empty nuka bottles and victory and quartz ranger helmets

sensor modules, turpentine, scrap electronics, ingredients for weapon binding ritual, large whiskey bottles, mutant cave fungus, Legion coin, vodka, whiskey, dynamite, chess boards, purified water, white horsenettle, golden gecko skin, psycho, med-x, mentats, turbo, boomer outfits, boomer hats, atomic cocktail, tomahawks, throwing hatchets, jalapeno peppers, gecko meat, banana yucca fruit, pinyon nuts, lunchboxes, cram, instant mash, cherry bombs, and anything useful I can lockpick.

If you could play them I'd collected hundreds.

Cigarettes. Packs, Cartons, or Individual ones, doesn't matter.

My NCR character collects the helmets of the higher ranking Legion soldiers he kills. Figured it counts even though you said leave weapons and armor out, because he doesn't collect them to wear/sell them. He keeps 'em as trophies.

Oh boy, I'm the King of Detritus.

Flour
Cigarettes
Pre-War Money
$100 NCR dollar
Various childrens toys (To decorate the 'Den' room of the Lucky 38 Presidential Suite)
Unique Weapons
Unique Armors
Unique sized misc objects
Absinthe
Vault Doctor clothes

I collect teddy bears and arrange them in weird positions, like the easter egg in F3 in the sewer waystation where you find the oddly placed bears. And Dino toys and rocket ship. I just like the little kid toys and place them around in places.

Nothing. My patience does not extend to arranging loot into positions nor my carry weight allows picking every item up.

I started collecting those silly NCR Ranger helmets and line them up in my Legion safehouse.

I collect everything that isn't weapon, useless book, or plant-picking related. Nuka colas, teddy bars, toy cars, money, dinos, smokes.
I don't always collect every single one of the same item, however. eg., I try to get at least one of every clothing/armor item (1 of each baseball cap, 1 of each Fiend outfit, 1 each of Pre-War clothing etc) but don't need more than that.

I also don't arrange the arrange the collections all over the room since I have no patience for doing that to 10000's of items. They just get stuffed into chests & drawers with the occasional dozen or two tossed the bed or floor so my companions can kick them out of the way when they're wandering around the room.

Within my inventory and Boone's are 10 loose cigarettes, 2 dino toy and a sunset star deputy badge (likewise, a badge on each of my companions... if only they were wearable). As for collecting: anything my character not only used but relied upon as to equipment and then also trophies of declared opposition (ie. Benny and Elijah at least).

Ammo,
Gnomes,
Teddy bears,
Toasters,
Nuka-Cola Trucks,
Brahmin Skulls,
NCR Dogtags,
TinCans,
Red/Green plates,
Coffe Mugs,
Pre-War books,

01.) As a hold-over from Fallout 3, I collect every teddy bear I can find, and arrange them everywhere in my residence, before piling the rest onto the bed.
02.) I collect one of everything there is, but keep them arranged in appropriate containers. Cigarettes are a disgusting exception, and always get sold.
03.) I'll collect one of every type of cookware there is, and arrange them in the kitchen. This includes 2 of every type of plate and utensil.
04.) I have a strange thing for collecting all the flour I can find, and adding it to my food. I'll also arrange a large banquet if space permits.
05.) All pre-war toasters are saved. Post-war toasters are discarded.
06.) A library with one of every type of skill book and ruined book there is. All pre-war books get saved period, with one of each color and size displayed.
07.) All Nuka-Colas get saved, and I never drink them. Quantum chemist is a must. I don't care about Sunset S., but will save them anyway. Sometimes drink.
08.) I collect one of every type of weapon, and repair them to 100% over time. But I never use any of them, and they mean less to me than, say, dinner plates do.
09.) My bar - it's one of every type of alcohol there is, arranged and displayed. I'll collect them as well, but keep them in containers.
10.) One of every type of outfit there is, repaired to 100%. I'll keep extras if I wear them all the time, like Field Hand Outfit or Headwraps.

While we're at it...

11.) One of every type & color of head wrap. I'm contemplating an entirely new play-through, because I 'repaired away' many different ones unknowingly.
12.) Animal hides are collected, but also neatly arranged as rugs and locker coverings. They fit neatly together, and you can carpet a whole floor with them.
13.) 'Differently sized' items. 'Unique' items of a size that's not normal always get saved. The Deluxe had a lot of cookware like this.
14.) Woodchippers. I can't explain why.

I've never actually seen games like Second Life before, but my boyfriend won't even let me try them. He says my head would explode.

I was never to be able to get rid of any gun ammo even though I only use like the same 3 weapons each time I play.