One of the first things in D&D with which players and DMs become jaded, I think, is the "plus something" model of magical weapons. At least, that was and is true for me.
The whole "plus something" weapon mechanic smacks strongly of what I've come via the OSR to understand as an effect-first mechanic. It exists not to model any particular fictional power of a weapon, but to grant bonuses to attack and damage rolls. While that does allow DMs and gaming groups to decide for themselves in post-hoc fashion what exactly those bonuses represent, that's addressed barely or not at all in the rule sets with which I'm familiar. Moreover, any +1 weapon is as good as any other +1 weapon of the same type, regardless of the "fluff" any particular DM or setting attaches to it.
The "plus something" model also contributes to inflation of the power curve and the devaluation of magical weapons in general. You stick a +1 sword in the dungeon, and the party finds it. That +1 to hit and damage seems pretty trivial right now, but remember that it applies to pretty much every opponent the sword's wielder might face. It's universally effective. There's little or no reason why anyone might want to use a different magical weapon based on in-game circumstances. So where do you go from there when you roll up the next treasure hoard with a magical weapon? Once everyone in the party who can use one has a +1 sword, any further one you might place is just redundant, and you either have to allow them to sell it or make excuses why they can't and have them accumulate closets full of weapons for which they have no practical use. ("Another sword +1? Just put it with the others.") One solution is simply to be very, very stingy with magical weapons, but unless there are cool non-magical things on which to spend loot with purely monetary value, a dearth of magic makes finding a hoard of treasure a ho-hum experience. Or, you could grit your teeth and start placing +2 swords...
Sure, there are other powers to add to weapons, especially in the Expert Set and onward. They certainly add some welcome variety, but in the rules as written they're always applied to a platform of plus-something. You don't just have a sword that flames or extinguishes flames, you have a sword +1 of flaming or a sword +2 of extinguishing. In other words, it's just more power creep as powers are stacked on top of bonuses.
Instead of starting with an assumption of pluses to hit and damage, what if we started with none at all? Attack and damage bonuses wouldn't have to be done away with entirely; they simply would not be present in every magical weapon by default, nor would an attack bonus and a damage bonus necessarily be present in the same weapon. Attack bonuses, damage bonuses, and other mechanical effects can then be applied to weapons based on a meaning-first construction.
Hero weapons: Formerly wielded by great heroes (or villains), these weapons have absorbed some of their wielder's combat prowess. When used by a new wielder, this knowledge is imparted subconsciously - he finds himself able to anticipate his opponent's moves and counter them with techniques of a more seasoned warrior, conferring a bonus of +1 to +3 to attack rolls.
Rune weapons: Inscribed with the runic true-names of particular species or types, which hold power over those creatures, these weapons deal +1 to +3 damage against the appropriate creature type only. A dragonbane sword does extra damage against dragons, while one inscribed with the rune for ogres does extra damage against them. The runes can be deciphered, and thus the weapon's properties deduced, with a read magic spell.
Flaming: The blade or striking surface of the weapon will burst into flames (possibly strangely or spectacularly colored) on command or when a specific condition is met (i.e. the sun is out or undead are near.) The flame causes extra damage (either +1 to +3, or double, or roll twice take highest) to creatures notably vulnerable to fire, like yetis and white dragons. It may also ignite flammable materials (10% chance per hit in combat).
Holy: The weapon can strike unholy and blasphemous creatures, such as undead, which are immune to normal weapons.
Wolf-bane: Made of enchanted silver with the durability of steel, and capable of harming any creature that can be harmed by ordinary silvered weapons. Especially appropriate if ordinary silver weapons in the campaign are subject to damage or wear.
Enemy detection: When hostile creatures are near, the weapon emits a glow or vibration, the intensity of which is proportional to either the magnitude of the threat or the proximity of the enemies. May also be a feature of rune weapons, indicating the presence of its target creatures. The swords in Tolkien's Middle-earth which glow when orcs are near are a good example.
Bound spirit: The weapon holds a bound spirit of some sort, such as a demon, angel, ghost, or elemental. Powers conferred on the weapon could be nearly anything, and the bound spirit may exert influence or control over the wielder, either subconsciously if the spirit is dormant or non-sapient, or consciously in the manner of an intelligent sword.
All sorts of other effects are possible, of course, greater and lesser, combat and non-combat. Light, invisibility, energy drain or defense against it, charm, detections of various things, stunning, paralyzing, poison, fear, and more are all viable, useful, and interesting powers for weapons. There's no reason at all that these couldn't stand on their own, without the need for an underlying plus-something bonus. Rather, they should be on equal terms with attack bonuses and damage bonuses, with none considered "must have" or essential to the very concept of magical arms. In doing so, the potential for variety is expanded, and the potential for power creep is lessened. A "hero" sword with +1 to hit is distinct from a "rune" sword with a +1 damage against orcs or a flaming sword with no pluses at all, without any being objectively and universally "better."
It might be worthwhile to cobble together an alternative magic weapons random table using this philosophy. Is there any interest in such a thing?