I am looking into this now, and it appears that the effects can be randomly assigned, but they are also usually connected to various weapon bonuses. It appears that the dripping blood effect is from life steal or health generated per second. I can confirm that my weapon has the effect and mine has life steal.
Here is a nice showcase of all the effects, sadly it does not say what caused them.
Furthermore, as quoted from Blizzard (Bashiok):
They're low level items with low level elemental effects on them. It wouldn't be very awesome when you find a super insane weapon later and the elemental effect looks the same as a level 10 item, would it? :)
This basically means the more powerful the elemental power the brighter the glow.
- The effect at 0.05 is associated with Cold damage. (Possibly more)
- The effect at 0.08 is associated with Fire damage. (Possibly more)
- The effect at 0.16 is associated with Poison damage. (Possibly more)
- The effect at 0.21 is associated with Arcane damage. (Possible more)
- The effect at 0.29 is associated with Lightening damage. (Possibly more)
- The effect at 0.35 is associated with damage dealt is converted to life and life steal (Possibly more)
- The effect at 0.41 is associated with the "Of Storms" item tag. (Possibly More, also, this is considered lightening damage as well)
- The effect at 1.13 is associated with Holy Damage. (Possibly more)
It also important to note that other effects can overpower each other. I will try to provide examples as they present themselves.
- Arcane is overpowered by the life steal glow. (It seems)
- Chance to freeze on hit is overpowered by life steal glow (It seems)
- Poison damage is overpowered by life steal glow (It seems)
It seems as though life steal trumps all glows.