Choose or roll (1d10) on the following table. Most results will need to be fleshed out to some degree. In general, the more powerful the weapon, the more or stronger its quirks should be.
1 Activation requirement: The weapon's powers only function under a specific circumstance, which usually involves the user performing or abstaining from some action, e.g. the user is drunk, singing, has not committed a sin in the past day, has stolen something worth at least 50 gp in the last day, taunts his opponents in rhyme, washes his hands in holy water before handling the weapon, etc.
2 Ethos: The weapon has a code of ethics. This could be a traditional alignment, or a commitment to uphold or defeat some other ideal or virtue - beauty, truth, justice, compassion, courage, etc. If the weapon user tries to take action which is opposed by the weapon's ethos, it may inflict damage on him as a punishment, or a penalty or curse may be imposed until the weapon is relinquished or some atonement is made.
3 Favored wielder: The weapon prefers a certain type of person to wield it - a certain class, race, sex, religion, group affiliation, appearance, temperament, etc. If the character wielding the weapon does not meet these criteria, the weapon may inflict a curse on the user, or its magic may function at a diminished level or not at all. The weapon may even gradually change the user to fit its ideal!
4 Glory seeker: The weapon's combat powers only function when the user is fighting the most fearsome opponent present (or earnestly trying to fight it, e.g. cleaving a path through its legions of mooks toward it.) May not function at all in a given combat if none of the opponents are particularly fearsome.
5 Jealous: The weapon will force the user to relinquish all other weapons by inflicting some curse upon him or her for as long as the other weapons remain in possession.6 Monster attraction: The weapon calls silently to monsters (either monsters in general, or a particular kind.) While the weapon is in the possession of the party, random encounters occur at twice the normal frequency.
7 Operating costs: The weapon must consume valuables - gold, silver, platinum, or gemstones - in order to function. (Specific type and amount at the DM's choice.) If it misses a "feeding," its powers go dormant until it is fed. If allowed to remain dormant for a long time, the cost to reactivate may be greater than normal. May be dormant when found - nobody's feeding it while it's lying around a dungeon.
8 Report: On every successful attack, the weapon makes a loud noise - a thunderclap, a trumpet fanfare, a scream, maniacal laughter, or whatever noise seems appropriate. May attract wandering monsters, and certainly spoils stealth.
9 Soul eater: The weapon must be used to slay a creature of at least half the user's HD every day, or its powers will fall dormant until the next kill.
10 Wax and Wane: The weapon's powers expand or diminish according to some regular cycle, such as time of day or year, or phases of the moon.
For more possible hindrances and curses, see this post.