Mulch around your plants with a Newspaper barrier followed by composted mulch to control weeds and grass in your garden.
From an Internet gardening page:
Q: I heard you can put newspaper down over the ground to control weeds and then top it with wood mulch. Is that a good idea?
A: Sure is. Newspaper is wood, too - just in skinny form! In new beds, I use whole sections of it myself right after I improve the soil with compost and rake the bed smooth.
I throw a pile of papers in a wheelbarrow with water so they're soggy when I place them. I slightly overlap the edges and use an average section that's about 8 pages thick. After I lay a section of newspaper, I top with 1 or 2 inches of bark mulch and keep working in sections as I go along. I do that so the wet paper doesn't have a chance to dry out and blow around before I can top it with bark.
The paper eventually will decay and add nutrients and organic matter to the soil. Earthworms like it, too. The sections also help hold in moisture and do a great job at choking out weeds. It lets me cut down on the amount of bark mulch I need to buy. Instead of using 2 or 3 inches of mulch, I use paper and only 1 or 2 inches of bought mulch.
Use regular newsprint, not the glossy flyers and such.