I have heard some conflicting info on this, but mostly "about 3 inches deep" is what I remember. Are there some veggies that need more than others?
Well, one thing to remember is that you can have a garden with no mulch and you can have a garden with a few feet of mulch.
Make sure your mulch doesn't just take the place of weeds, it shouldn't compete for light and inhibit nutrients from entering your plants. It should be safe and in the right quantity to till in (or at the very least leach in) to your soil. If you mulch with certain things like pine needles or leaves, you'll add acidity to your soil, which you'll need to neutralize. If you mulch with paper or plastic you don't need 3 inches, but you do need to make sure it doesn't fly way or harm your plants. If you're using yard waste to mulch, try to do it in a way that doesn't put tons of weeds in your garden.
3 inches may be used as a minimum to inhibit weed growth and a maximum to allow water to flow through (especially if you're using leaves). It's not so much that some veggies need more mulch, its more that some veggies are smaller than others and don't thrive in the same depth of mulch.