AcornMan

I just bought a mountain bike with hydraulic disc brakes, the first time I've ever had disc brakes. I noticed almost immediately that the disc on the front wheel scrapes against the brake even when I'm not putting pressure on the brake lever. After a long ride today, it was especially bad. Then after a few hours of sitting in my garage it didn't to it until after I squeezed the brake lever. Not being familiar with disc brakes, I'm not sure whether this is normal, but it sure doesn't seem like it should be happening. Any advice? It's a new Specialized bike, so I would think the brakes are good quality.

cobba

Continual rub or intermittent rub?

If you have continual rub try realigning the caliper.
If you have intermittent rub you rotor probably isn't true and will need truing.

Andrew R Stewart 

True rotors, carefully centered calipers (pads), calipers parallel to rotors are the key aspects of rub free brakes. However the pad retraction consistency and amount are also important and can vary during use. In a hydraulic system the pads are retracted by the vacuum within the pistons (the master piston is pulled out by the lever and the caliper/slave piston is pulled inward in response) as well as the "rubber" seals that the slave piston has within the caliper's cylinder. So any grime that collects on the seals can hinder that piston's movement. Additionally a system that is over filled with fluid will cause the pads to be too close together without any lever movement.

We often need to clean the seals (we use Clean Streak after removing the pads), squeeze the pistons back into their cylinders (using a clean cone wrench between the pads) then re seat them by pumping the lever and sometimes find a need to bleed out a drop or two of fluid to get enough pad gap or to balance the lever pull amounts between both levers.

For all their neat aspects disk brakes can be more sensitive to rub and require more frequent fiddling with then rim brakes do. Andy.