This is a little something I really liked while we played the German Midgard RPG back in the day. Everytime a character's main weapon dealt a critical hit the player had, at the end of the session, the chance to give a small part of his soul into the weapon (and make it a personalized magic weapon). To that end the player had to roll a d100 on a table similar to this one (I changed it a bit for D&D):
1-93 no effect
94-95 +1 to hit against enemy slain*
96-97 +1 to hit
98-99 +1 to damage
100 personal effect related to the incident and a re-roll**
*Happens just the one time and against the enemy the weapon was used against when the critical hit occured. It stays fixed on that type of enemy and may only increase if a another critical hit against that type of enemy is cast (and the d100 comes up with 94 or 95).
**The second time this happens, it increases the first effect, the third time the weapon will get a name and there is a 40% chance (minus CON) that the weapon takes a great part of the character's soul after the owners death (the effects do not vanish in that case). This chance will increase by 5% every time this comes up again.
The results stack, of course. And the magic works only if the owner is wielding it. If the owner dies and the weapon has no name yet, all powers it had are gone. If the bonuses stack to a +5 all in all, there is a 5% chance for every +1 to remain in the weapon (now usable by everyone wielding it).
I like to let the players make the roll (it's something they are looking forward to). But if you roll it as a DM, it might have some positive aspects, too (just from a narrative perspective, I guess).
It might be a good idea to involve clerics in this a bit, like encouraging some rituals or weapons cults to increase the chance to "load" the weapon with pieces of the owners soul (character smites foe with mighty 20 + cleric makes a fuss about it = +1 to +5 on d100).
It's not much, but the players liked it quite a bit. And in the long run, they might have a very personal magic weapon they can call their own. With a history and all that.