Vinegar is claimed to be a good cheap "organic" weed killer especially for young weeds. It may not work on old established weeds. However, you are still spraying vinegar on your garden, which might not be the best thing as it has to go somewhere. Its eventual fate will depend on dilution and evaporation. Probably the absolute safest truly organic method of weed killing is to simply pull them out, or turn them into the soil every week or two. A selection of "organic" and "least-toxic" weed killers are listed at Planet Natural in Bozeman, MT, USA. A web search turned up a New Zealand company that offers an "organic" weed killer called Organic Interceptor made of pine oil. It's a bit expensive and while natural, it is not totally benign. Finally, the classic "Roundup" glufonsinate-based weed killers, are pretty close to "organic" as they are soil based, and break down immediately on hitting soil.