I have to weed the garden about once a week. The weeds keep popping up but as long as I stay on top of them they aren't a problem. Except for one. The bane of my existence and arch nemesis is Canadian Thistle. Canadian Thistle spreads though an underground network of roots. If you pull the thistle and break the root you have not gotten rid of the plant but allowed the root to split and produce two. Canadian Thistle runs rampant, will push its way into any open space, and can grow anywhere. I think even during atomic warfare Canadian Thistle would be the only surviving organism.
My first year gardening I pulled the weeds and doubled my problems. So last Summer I started by using an organic natural spray to spot treat just the thistle and kill them. But this quickly became pricey and they just kept coming. So I started just snipping off the leaves at the soil level. This doesn't get rid of them and they do come back at the same root. However if I catch them while they are small it does keep them at bay. I've tried boiling water which seems to work well but now that the garden is planted I would be killing off my vegetable plants also.
An excellent example of how much of a terrorist this plant is. This one has managed to grow into the wood and push through the paint on our privacy fence.