Poor soil and hungrier plants demand the most nourishing mulch. So every year, compost gets slathered an inch thick over the ground where vegetables grow.
Buckwheat hulls, straw or wood chips are adequate and attractive for most flowers.
DON'T WALK ON MY BED!
Of course, you can't just stop tilling, throw mulch on the ground and garden as usual. Walking on the soil and rolling a wheelbarrow, garden cart or tractor over it compacts the soil; tillage is then needed to aerate it.
The way to avoid compaction in the first place is to lay out the garden with permanent areas for plants and for traffic. Trafficked areas also need to be mulched, in this case with some lean, weed-free material such as wood chips, gravel or straw.
Planted areas in my vegetable garden consist of rectangular beds 3 feet wide surrounded by 18-inch-wide paths. Beds in my flower garden are more free-form or have stepping stones.
Planted areas in a vegetable garden don't need to be raised beds, however; they can be laid out flat on the ground.
A big advantage of bed planting is that you can pack more plants into less space. Instead of planting carrots with 18 inches between rows, four or five rows can be planted with only a few inches between them. (That 18 inches is to let you walk between the rows for planting, weeding and harvesting. With a 3-foot-wide bed, you can do all that from the paths.)
Also, different vegetables, flowers, or vegetables and flowers can be grown together in beds.
DRIP THAT WATER
Changing watering technique was the final step on my road to "weedlessness." Not all plants need regular watering, but for those that do, drip irrigation is the way to go.
Drip irrigation puts water near garden plants, so none is wasted or promoting weed growth in the areas between plants or in paths.