To avoid using a mop, get down and dirty with your floor. Depending on the type of spill you are dealing with, a small bowl of soapy water may be the most you need to clean up the mess. Dip a sponge or cloth into the water and scrub up the spill. For spots like coffee drips or a heel scuffs, wet your sponge or cloth in the sink, apply a dab of soap or cleaner and wipe up the spot.
While vacuuming will not remove stains or spots, it will get up dry spills and any dirt or dust on the floor. Vacuuming regularly can also extend the time between moppings and keep the rest of the house cleaner by eliminating tracking. Keeping hard floors vacuumed also extends their beauty, as small grit can ruin the finish and cause tiny scratches in the surface. Choose a vacuum or floor sweeper without a beater bar to keep from causing damage to your floor's surface.
While it may sound like it comes straight from a big-screen action thriller, robotic vacuums are now available that use a special cleaning solution to wash your floors without you. They are left running continuously and pass back and forth over the floor, killing bacteria as they go. They are ideal for kitchens and bathrooms.
If it is not so much the mop you object to but the time it takes to prepare a cleaning solution, sweeping up beforehand and then waiting for the floor to dry, a dry mop equipped with a cloth may be just the solution you are looking for. These sweepers use static to pick up dirt and debris off the floor. Passing one of these over your floor every day, while ineffective against spills and stains, certainly keeps the dust and dirt at bay.