I started an experiment last Fall that I am very happy with. I have been experimenting with a permaculture concept- a combination of green mulching and interplanting with flowering plants that attracts beneficial insects. In the past I have either weeded diligently or mulched heavily with some kind of prebagged mulch or hay to suppress all the weeds.
I have changed my mind about "weeds" and realize that most of them are probably good for one reason or another. Either they attract beneficial insects, or they bring nutrients up from the deeper soil that will be released back into the garden when they decompose. This year I decided to only weed out grasses (which have shallow root systems that compete for nutrients with your garden pants) or things I really did not want, like burrs.