Don't have anything in particular I need to kill, just wanted to make a good list to spark people's imaginations so they don't feel so reliant on products. Let's list methods of non-chemical death, besides pulling/digging/spraying anything, (whether the label says organic or not - not a discussion about ANY products or salt or vinegar or gramma's homemade recipes.)

smothering plants or whole areas with ____ (whatever)
pouring boiling water on
tying a plastic bag over
putting an upside-down pot over
removing foliage whenever you see it
step on every day
cover with a large rock or potted plant
allow to dessicate during drought (make sure you're not irrigating it)
cover with mulch/compost pile
yank it out with a chain tied to a truck (call "call before you dig" if you don't know what the roots might be wrapped around!)

Different methods for different enemies, climates, and proximity of other plants, of course, but there's usually a manual way.

Unfortunately, manual methods are usually micro-methods, often not applicable to larger areas, but hopefully useful to those able to micro-manage some or all problem plants.

What else?

cut below ground level.

On the farm where I grew up pigs in confinement would destroy all vegetation except Datura stramonium (Jimson weed).