One of the rotor dust shields probably came loose or got bent when you took everything apart. Reach in behind the rotor and you will feel a thin metal shield just behind it. Try to wiggle this shield. If there is any play at all, this is where the noise is coming from. You can usually just bend them back into shape if they are bent, or thread the bolt through a larger washer if it pulled through the hole.
I have had to re attach all 4 on my car in the past 2 years, took 2 off of my girlfriends car because they were falling off, and one on my mother's car. It's a pretty common problem.
This is the simplest explanation. Especially if the brakes don't make any noise while actually braking.
When you installed the new pads, did you use silencer shims? They don't always come with the (cheaper) pads. That is most likely the problem, if there was no noise before their replacement. Otherwise, check your wheel bearings.
Could be your muffler bearings or canutor valves are shot.
I have a 2006 - Toyota Matrix
I recently replaced my two front brake pads.
Shortly after replacing them, i started to notice a "rattle" sound coming from my front drivers side whenever I drive over bumpy roads.
Normal driving there is no sound, and my brakes act normal / well.
There are also no noises when the brakes are applied. I only hear it when driving over bumpy roads
So, to me it almost sounds like the brake pad is somehow loose. Like as if the hydraulics that push the brakes into the rotor retract too far when your off the brake, allow the pad to rattle.
Any thoughts?