For the purpose of this discussion, we're not talking about boring things like Healing Potions or Wands that aren't much but placeholders for having actual wizards and clerics around, or things that just aren't very exciting like the Boat of Folding. We're talking today about the venerable, boring, blank +1 Sword.
"This is a generic magical item," is what Boring Plus One Sword says to you, "I have no backstory and do nothing but give you a bonus on your attack and damage rolls. I am otherwise a normal sword."
The problem, if it wasn't obvious, is that you have the phrase "generic magical item." There shouldn't be a "generic magical item" any more than there should be "stereotypical dwarves" or "boring-ass wizard" in your game. It doesn't mean that every sword that you find has to be a +4 Holy Avenger or a +3 Sentient Flaming Sword. We're talking about making items interesting, not making them "awesome" or "cool" to the point where everybody's running around with high-powered items and you've gone from Boring to Overload.
Let me give you an example I particularly like (if I may be so bold as to post my own work):
Leaf-blade Arrows (Unique): This bundle of ten +1 arrows was crafted by an elvish wizard and are made entirely of wood, with a leaf-shaped head. They are as hard as iron and will not burn.
And there you go. You now have interesting +1 Arrows. Not super interesting, but there's a couple of things in there that mean that these arrows have a history. They have a purpose. They're magic.
Another example, this time from the basic Labyrinth Lord book:
Sword +1, locate objects: The wielder may locate objects as the magic-user/elf spell one time each day, to a range of 120'.
You have a sword that's still a +1 sword at its core, but now you have a magic item with, again, purpose. The wizard who made this clearly had a spelunking, tomb-raiding accomplice he made it for. Or maybe somebody who kept losing his spellbook? You can picture the guy who made it, you can imagine who he gave it to, and most importantly, it reminds you that this weapon is magical. You can have really sharp, really mundane sword, but how many swords find your car keys for you?