Mow over them, but first note if any seem to be growing in a circle. Mushrooms growing in a circle frequently indicate a disease inside the circle.

A mushroom isn't an indication of a specific disease, though it may look that way for awhile. It's just a matter of the fungi doing so much decomposing that the grass may end up nitrogen starved for awhile. If you've ever had a fairy ring, you'll notice that the grass gets really DARK green first, as the decomposing is at its peak. The fungi then has to move out further to more fertile ground, leaving hungry grass behind. If any grass actually dies within that ring, it's usually because the fungus organism has been able to build up such a heavy (underground) mat of mycelium that water (etc.) can't penetrate any more.

Please know that the fungus is within the soil, out of sight and out of reach. The mushrooms are merely temporary fruiting bodies, appearing only to disseminate spores. Mowing them rather than raking them up could be like overseeding your lawn with mushroom spores! Unless you can get to them while they are still immature and the spores haven't developed.