Magic Items Are All Artifacts

My approach to magic items in fantasy RPGs - even the lowly +1 sword - is to make them all special. While so-called Monty Haul campaigns filled with treasure both monetary and magical was fine fun when I was a teenager, it became one of the elements that turned me off D&D in later years. Not that you HAD to liberally pepper your adventures with treasure, but the game definitely pushed in that direction, with important bits of treasure even under the most unassuming of straw beds throughout the published adventure scenarios. In adapting those scenarios for my games (and often for other systems), I would make a lot of that stuff disappear, so as to make treasure, the magical kind especially, more rare and noteworthy.

But treasure scarcity cannot do that job alone. Just how special and noteworthy is that rare magical item when it turns out to be a boring old +1 short sword or +2 ring of protection. Useful sure, but simple statistical bonuses have no flavor whatsoever, and can easily be thrown away when that +2 short sword comes along. So boring. That's why my approach is to make each magical item completely unique, i.e. treat it as an artifact. I usually add 2-4 of the following components to a run-of-the-mill, stats-buff, magical items:

A name: If players talk about +1 swords with their characters' voices, you've failed. Just think of the swords in A Game of Thrones - Ice, Lightbringer, Longclaw, Needle. How much more epic those are, how they might reveal something about the character wielding it, and how they might contribute to the character's reputation. A character would sell off a +1 sword easily, but her famous Stormbreaker? Not so sure. Depending on the situation, a GameMaster might let the PLAYER name the item.

A story: Whenever possible, magical items should be part of some legend or at least a dark rumor, giving it a place in the world's mythology. Who did it belong to before? How was it crafted? How was it used? Making magic items more scarce means an item can be the pay-off of an adventure, and the players will have heard of it during the adventure. It will be the big bad's weapon, or lie in the tomb of a fallen hero. If that's not possible, having an old sage "read" the item should offer up some flavorful morsel of information. And of course, the characters are invited to add to that legend...

A look: Magical items shouldn't look generic. They should have runes and engravings, sculpted pommels, eldritch materials, some distinguishing mark that marks it as special.

A special effect: This is probably the most important and fun because unlike the other three elements, it will come up in play with each use. Working from its name, story and/or look, assign each item an effect that represents the manifestation of its magic bonus. Maybe it glows unnaturally in battle, or feels hot to the touch, or makes the user's veins darken on his arm. Think of famous magic items from fantasy novels - Elric's blade hums eerily as it thirsts for blood, Frodo's ring of invisibility changes the world around him into a fierce, ghostly place. These do add a game effect to the item, if only to its intimidation factor, but you should embrace it. If a player wants to blow out a candle using his sword's special effect of throwing up a gust of wind when he pulls it from his scabbard, then let him (alternatively, it may be an unwanted consequence of pulling his sword in some situations). Not only does this reinforce the uniqueness of the item, but it takes the sting out of how rare magic items are.
Upgrading artifacts
For campaigns that stay around the same basic levels, that's all fine and dandy, but obviously, as campaign levels rise, so should the characters' equipment. New items will be found, and the old ones just won't cut it against tougher opposition. Players have several story options open to them that give respect to the old item and its stature in the world's mythology. They might bestow it on an apprentice, henchman, or otherwise favored NPC. The legacy goes on even if the character has grown out of the particular object. The player can also choose to store it in a prominent place, like a temple, a friend's tomb, or a stronghold. Or the character may hold on to it and keep using it, perhaps in her off-hand, or as a finishing move, strictly as a personality quirk.

Of course, the GM may play a hand in it, for example destroying an item in spectacular fashion knowing full well it can be replaced by a better one in the treasure trove ahead. However, here's an idea that seems to me no more manipulative of the source material than scaling back the amount of magic made available to players (and in fact, may help explain it): What if items of the same ilk (as vague as "swords" or as specific as "bastard swords" could sap each other's powers, perhaps through some magical process or ritual? It would allow the character brandishing a +1 "Stormbreaker" to find a +2 sword and simply MAKE Stormbreaker +2 instead of trading up. Stormbreaker gains the better bonus (and powers like vorpal blade, presumably), and the other blade is destroyed or rendered inert in the process. It might even occur naturally, with one item draining another without the need for external magic (though in limited, resting conditions). It's a way for your weapon to level up with you, and as your legend grows, so does that of your weapon, armor, etc. I wouldn't recommend it for every item or effect, but if we're talking about boring old stats bonuses, I definitely am.