I really like this idea. The sentience implies personality which may also implies preference, as some have suggested.
While I agree it shouldn't be something industrial, I think perhaps a player in adventurer mode should be able to make one by, for example, deliberately imprisoning a demon inside his axe, and the demon, being a demon, can benefit or harm/inconvenience the wielder based on the actions s/he performs.
For example, if you trap a demon in an axe, the demon may enjoy a good elf slaughter and enhance the blade with whichever powers he once wielded, be it fiery, blistery, or chillingly goodness (badness). Such a demon would likely be imprisoned in the axe by force and submission and some trapping mechanic. On the other hand, it may be a deal was struck with the demon, or he was tricked into voluntary imprisonment.
Similarly, a force of good may be invited into the weapon by some deal or other. If you kill bad guys, you gain ++, if you kill good guys, the blade becomes unwieldable or something.
On the other side of things, it may be that an already exceptional item simply awakens to sentience by divine endowment or unconventional circumstance. Perhaps a preposterously long life of killing goblins, as was suggested, might realize it's "purpose" and waken to a personality which develops thereafter in accordance with its wielder and the actions in which it is involved.
I like Gitsnak's notion that the souls which pass through the item impact it, so that it may be corrupted or gain power by, say, resting tenderly in the heart of a dragon in its death throes, as it thrashes wildly, as its blood pools and drains away, as it shudders finally with a hateful snarl as a snide dwarf gloats over (under) and leaves the body to rot, festering in its hate and anger, pouring its soul into the blade of its demise so that it may one day be be used against the tiny horrible creatures. Perished but immortalized.
(blade causes unhappy thoughts if the wielder is a dwarf, and also burns the wielder's hands with dragonfire. Enjoys killing dwarfs and setting them aflame.)
edit: Actually, that's probably not what you meant. I think you mean the item has its own sentience and not any necessarily the sort of borrowed sentience of being possessed. Didn't mean to imply that what you suggested was the possession thing.