My fallout 3 characters inevitably wind up looking like mad max. Typically, this means wearing the shitty leather armor and a motorcycle helmet (My DT is always shit) but it doesn't matter... cuz mad max.
The dog (or pet). Not so much of a misc item, I know, but I have to have the dog with me at near all times (unless stepping into an area that I know is far too dangerous for him).
Dogmeat (of Fallout 3) will forever be one of my most cherished video game characters. I've spent hundreds upon hundreds of hours with him.
Same goes for EDI in NV. Taking Rex just didn't feel right. He belonged to someone else.
I'm starting to really like Meeko in Skyrim, as well. Though never as much as Dogmeat. One reason being Meeko never shuts the hell up...
I noticed that I seem to fight a lot harder when the dog is with me. I have to make sure he isn't killed!
A bit more on topic, though. I'd say glasses. My character needed his glasses. Never took them off (except to sleep). Oh, and in FO3, he always kept his old BB gun on display next to his old baseball bat and cap in his Megaton home.
In Fallout 3, Ms. Nina always had her headwrap on. Always. Even though she switched from her armored vault suit to combat armor, from combat armor to T-51b power armor, and then to a merc outfit when she was so high level nothing could touch her, there was always that headband.
I always carry around a wrench and basic tools with my character Roderick in New Vegas. At minimum the wrench. He also brings along ED-E and Cass, his lovelies. I also enjoy wearing a combination of the Ranger Grey Hat, aviator shades, and Kings jacket. Looks amazing.
For me, it was always in Fallout: New Vegas. After completing Legend of the Star, the quest where you collect 50 Sunset Sarsaparilla Star Caps, I would always carry around one of the little Deputy Badges everywhere I go. In fact, I'd make the point to pick all of them up, and make sure each of the companions you can recruit, ALSO carry one. Mainly because I pretty much always play the Very Good Karma NCR Supporter.
I also make the point to, usually, carry two sets of clothes. The armor I'll use for fighting, and a set of soft clothes for when I'm around others, like NCR friendlies. Those soft clothes usually include a beret and sunglasses.
I doubt hoarding one of every armor set, and one of every weapon, unique or modded, counts though. But I always do, keeping them in different containers around the Suite at the Lucky 38. Of course, that's separate from the armor and weapons I'll actually wear and use.
I still wear my iron helmet that you get at the beginning of the game when you try to sneak around the bear (I just charged the asshole though). And I have various little trophies that I keep in the chest of my house from really hard caves/dungeons. Oh and all the Thane weapons.
Bounty Hunter coat, grey ranger hat and "Authority" shades (to compliment my survivalist beard). That and my thrusty ol' 12 guage. Yes, my Fallout New vegas character IS a badass. For practicality reasons I upgrade to Ranger/Riot armour in the late game.
Fallout 3? Casual wear (some variety of merc outfit, like charmer), the shady hat Moira gives me and the turtleshell glasses that smug bastard burke has. He's a too cool for school kind of punk, with a fondness for disintegrations. Or that bounty hunter darth vader didn't want. He also carries around some knuckle dusters, in case things get personal. I have Charon and Dogmeat for company so I rarely have to worry about getting overpowered in my flimsy fabric armour.
Skyrim? Fur armour... cause it's cold up in them hills. I switch between a full body version and a lower body only version depending on the region I'm in. Also, Amulet of stendarr, cause with fur armour you need all the help you can get (blocking bonus). Also, Meeko is my constant companion.