What causes a lightbulb to explode? What causes it to make a loud pop and throw the breaker? I had a lightbulb break, but after I replaced it, everytime I turn on the light it goes "pow" and throws the breaker. What do I do now?

You have a short at the base of the socket which when energised overheats before the breaker trips and fractures the glass bulb... make sure that when you wired the new socket that the hot lead was to the center contact wire to the bulb. Also make sure the hot and the ground in the socket have no conductor filling the gap.....

I suspect there is a short in the fixture. Replace the fixture.

too many working appliances on that electrical circuit. the lightbulb is the weakest link. turn off everything and just keep the one circuit on at the fuse box. trial and error you can find which plugs are on which circuits. it is a long process, but rewarding when you are done.

I found this online: the only thing i can think of is a fracture in the glass, maybe the globes where both dropped by a careless shelf stock boy at the supermarket/hardware store
Suggestions for what makes a light globe explode include thermal shock by being hit by a hot fragment of material from inside, residual stresses, and extension of pre-existing cracks.
theres another good one actually, if there is an excess of moisture in the room for some reason, you may have condensation on the globe causing temp differences in different sections of glass when you turn on the light, sometimes this may take an hour to finally shatter the glass, sometimes it might be very soon after the globe is on, is the room unusually moist? or is there a spray bottle in the vicinity that may be getting sprayed in an upward direction at any time?...
oil or grease on the glass from touching the globe when you install it.
http://www2b.abc.net.au/science/k2/stn/newposts/2740/topic2740816.shtm

You might also check for 240V where there should be 120V. A common neutral may have come lose.