The washing machine itself could leak, so if you're on an upper floor, it should be installed in a pan with a drain, as shown in this picture. Better yet, tile the floor and have a floor drain installed. This way you'll be ready for any floods and you can mop the floor right into the drain.
The drying rack above the sink pictured here is a great way to save energy, but you'll want to get rid of the moisture in the air, so install a dehumidifier or an exhaust fan ducted to the exterior.
The closer your laundry room is to the rest of your house, the more sound will be an issue. If you are building the room from scratch, install batt insulation in the walls to reduce noise. These are heavy appliances that move around a lot. If the laundry is going to be on an upper floor, the floor joists should be reinforced to handle the load. Stiffening the floor will also reduce noise from rattling objects nearby.