with everyone who has suggested pine needles. They make a wonderful, fragrant mulch, acidify the soil, and break down slowly. As also mentioned above, organic mulches also improve your soil.
@frederick11 It seems like you're trying to re-invent the wheel with ideas about perlite, clay balls, etc. Nothing, repeat nothing, will totally eliminate weeds. Even if you pour concrete, they'll sprout in the cracks. You can control their spread by preventing them from going to seed and by pulling a few regularly as they come up, but they are always going to around to some degree.
@Sscape, I can't find any sources that back up your statements about perlite and vermiculite except for one study about sterilizing perlite for re-use in tomato crops which is not applicable to what you're contending. Provide us with cites?