I have an old saddle that I love, but don't use, on a wooden rack in my bedroom. It's not filled with sentimental value, but I like to look at it. I just wish I had kept the old Stubben saddle seat saddle that belonged to my grandfather that I used on my first horse. Also the tiny halter I had for my first horse's foal, born 10 months after I bought her. I could get sentimental about those!
I tend to be a bit of a pack rat, so I force myself to move along as much stuff as I can when it has lost it's usefulness. Blankets and safe tack stays; anything broken and outgrown by me, goes. I take meticulous care of my tack so it is rare that something needs to be replaced due to age or wear.
Sentimentally, I keep the halters my horses come to me wearing, and a shoe. The ones I have for resale don't stay long so I don't bother getting them nice halters with nameplates, but I do have all of their original halters. I keep them in a box and it's a nice sentimental bit without being to big or excessive (not to mention most of them are ratty and/or broken, so likely wouldn't find another use).
I am looking at my first saddle right now: it's on a display shelf in my bedroom. It technically is still usable but I don't want to use it anymore! Crosby Prix de Nations, ca. 1984, bought used by me in 1989. At the time I wasn't even riding but this was my "dream saddle" and a steal, so I snapped it up. To my chagrin I found out when I did return to riding in 1999 that flat saddles were OUT. Not to mention, darn hard! (I had never noticed when I was riding in a borrowed PDN as a teen) But I will never part with it as it was a fulfillment of one horsey dream... I still have to get the horse, alas.
I have the same saddle, my first as well and your post made me laugh because I had the same experience with flat saddles. Once in a blue moon I may ride one horse that it fits (his own saddle is also a pdn) but I long ago pilfered the stirrups and leathers off mine to use with my trainer's saddle, so my pdn hasn't actually been used in almost a year.
It sits in my task locker, but really should be moved back into my house.
A neighbor of my parents is a rider and lives in a gorgeous historic home. At the top of one level of stairs there's this little mini sitting room/alcove where she's displayed her old tack and ribbons and trophies. It's so well done, with shining brass and gleaming wooden display racks, I would love to have something similar in a future home, like a reading nook with a horse cooler as a throw blanket, stirrups as bookends (as someone else mentioned), the whole lot.