Strange that something you put on a salad should act as an herbicide, right? But here's the key: vinegar contains acetic acid. Vinegars with higher percentages of acetic acid will be more successful as organic herbicides. Unfortunately, the vinegar in your cupboard has a low percentage of acetic acid. It will still kill weeds, it's just that you may have to apply it a number of times (depending on the tenacity of the particular weeds).
If the idea of using vinegar as an organic herbicide really interests you, you can check at farmer's supply stores for vinegars that contain higher percentages of acetic acid. In my own test, I used regular household vinegar; my test subject was a dandelion weed (picture).
In this article I elaborate on the vinegar's limitations as a weed killer, how to use it and when to use it. And incidentally, while we're discussing things found in the kitchen that can function as organic herbicides, note that even boiling water can work pretty well on some weeds!
"Garden Safe" and "Nature's Avenger" are examples of organic herbicides. Garden Safe uses natural botanical pyrethrins, while Nature's Avenger is based on natural citrus oil.
But the problem with such commercial organic herbicides is the same as one encounters when using vinegar as an organic herbicide (see above): while these sprays kill annual weeds just fine, the tougher perennials weeds tend to hold their ground.
3. Organic Pesticide: Neem Oil
I had a good experience recently using organic pesticides. This spring, I became aware of an aphid invasion on my ninebark shrub. I used an organic pesticide named "70% Neem Oil" on the leaves. After spraying every 7 days for 3 weeks, I'm glad to report that I found no more aphids on the bush.
I've also had success killing aphids with Neem oil on the following plants:
Neem oil is also supposed to be effective against a number of other garden bugs, including Japanese beetles (picture), for example.