I almost always use up any cilantro I buy very quickly, so storage isn't often a concern. But a few months ago I accidentally bought more than I could use, so I placed a bunch or two, stems down, into a vase with water. I put it on an out-of-the-way windowsill, then completely forgot about it. When I finally looked over at it again - maybe 6-8 weeks later - Voilà! - it had grown roots. Not huge roots, but a quantity substantial enough for at least one or two recipes.
On a mildly-related sidenote, I had no herbs at all in house last night when I used some leftover roast chicken to make larb. The closest I could find in my fridge was the 2 inches of leaves left on the celery root I bought over the weekend at the Farmers Market. Celery leaves made a tasty, if inauthentic, addition to larb kai.
...defended from strong temptations to social ambition by a still stronger taste for tripe and onions." Screwtape in
The Screwtape Letters by CS Lewis
Fuckerberg on Food