My Lavellan keeps a Dalish Toy Soldier and a Wooden Wolf Totem (Token?) in her inventory. I headcanon that she's had them with her since the beginning. Her brother, the clan's first, carved them for her. They're an emerald knight and his faithful wolf companion. They used to joke that it represented them, but could never agree who was which, so they each carry one of each.
And I held on to that amulet from the Fallow Mire that has text attached to it. I keep hoping against hope that one day I'll find "R." and be able to give it to him. Or lay it on his grave. Whichever way it turns out.
Some of these little items just seem to have so much thought behind them. That bloody teddy bear. The engraved locket. They're surprisingly moving.
Whenever I completed Trouble with Wolves and get the Token of the Packmaster amulet, I give it to Solas. Because it's called "Zeichen des Leitwolfs" in german and well, he's the Dread Wolf, he can keep it for the rest of all my PTs. 
I also keep all Companion specific armors in the storage chest in Skyhold. I'd never sell Cole's Hat, even if I crafted a better one already.
I love this! Ever since you posted this, I laugh every time I look at that amulet. It's perfect. I also cannot ever sell Cole's hat, and put it safely in storage for him when he outgrows it.
Every trip to Skyhold sees the entire party re-tinted. I use a random number generator to choose which mats to use for each slot but everyone gets the same tints so if I use Plaidweave on cloth slot 1 on my Inq, everyone else gets Plaidweave in cloth slot 1 as well. Yes, I spend wayyyyy too much time at the tinting table and get some crazy looks, but they all match!
I determine when to move the main story along based on when I run out of dialog options with my LI, and yes, Skyhold has at least some nod regarding decor based on who I'm romancing.
But the silliest to me... you know that bag of gold on the bridge that explodes on your way to the Temple of Sacred Ashes? I go back and get it. Every time. As if the 45 to 55 gold is going to make a bit of difference long term. But, in doing so I find that sack by the cart so I feel justified.
I remember at one point I had an excess of plaidweave and had the whole party outfitted in the fugliest plaidweave and bright orange you have ever seen. They looked like the world's weirdest Scottish football team.
I decorate Skyhold based on who I'm romancing too sometimes! That's awesome. It was really weird when I was romancing Bull, let's just put it out there. (And the Par Vollen bed was just... no. I couldn't.)
I have to pick that gold up too. Every time. And to this day, I have to harvest everything I run past. Every elfroot. Every bit of iron. If I don't, I feel weird. It might be my OCD tendencies kicking in.
I always try to get as much court approval in WEWH as I can, even though I've played through it many times and know that I don't need all that much to get the job done. I do this with characters it doesn't make sense with, too. No matter their background or personality, when they get to the Winter Palace, the Inquisitor gets all cunning and charismatic.
In my first playthrough, I didn't quite get the importance of court approval in WEWH and rather hilariously, I think I had something like 35% approval. Because I would just go listen to Maryden play for awhile, or run around, or talk to Dorian, or be late. I just wasn't really concentrating on the approval part. Also, my first answers to Florianne were character-based so of course they were all awful (that Quizzy was very wisecracking and blunt).
So it was gratifying on my last, much calmer Quizzie, to finish WEWH with 98% approval (especially since this really does affect the political future of our worldspace.
Ahaha, I do this too. I always keep the wooden wolf toys valuables on my Lavellan and also always go talk to Solas untl he says "Vhenan".. No joke, one day I spent almost 10 minutes clicking him.
I've so been there. So done that. Yep. And it was worth it.
I hold onto the Wooden Mabari statue.
Me too! I keep that in memory of our sweet Mabari (whom I named "Houndwise") in DAO.
Okay so this may not be strictly on topic because it isn't in game but...I've been googling "Dragon Age 4" once or twice a day since I finished Trespasser on December 17th. I'm not alone, am I? 
Yeah, me too. I'm kind of... long-term obsessed. I love DAI like few things in this world. And it's awesome.
I'm guilty of buying all the mounts as well just because of my completionist nature. This made me think of another illogical thing that I tend to do and this is to walk around everywhere despite purchasing all the mounts.
Because party banter is worth trekking the land by foot (including the expansive Hissing Wastes)
Totally agree. I hardly ever ride my mounts, although the War Nug was worth it for the screen shots alone! Except for a few rare instances, like Hissing Wastes, I like walking -- it's less lonely and we get at least the possibility of banter. I love banter. (Also: I bought all the furniture too. Even if I was wincing at some of the beds and furnishings and going, "Really?")
Iron Bull is the only companion I'll allow to use a weapon with a Red Lyrium rune attached. I don't want any companions near the stuff, even if the runes are just a game mechanic to increase damage, and I don't even have a compelling reason for Iron Bull being the exception. I'm not his biggest fan, but I wouldn't want him corrupted either so it's not even something like that.
That's really interesting. I can't quite go that far (because I am a slave to dps), but it's really cool that you keep it logical that way.
I actually keep all of the "memorial" items in my inventory.
The most precious one was the crude notebook found in the camp of two survivalist infant sisters in the Exalted Plains, next to an active rift. There's no bodies nearby, but it saddened me greatly still.
I really love all of those too. One of the things that gets me -- and that I did in repeat gameplays -- was to stop at those moments and usually there would be a body nearby (and that I probably missed or didn't always notice in my first playthrough). The idea that we're reading letters and diary entries and these people DIED -- right here -- adds a level of real pathos to the game for me. They really do become people to me, real losses, not just loot opportunities, if that makes sense.