I read that vinegar works great.  Is it any kind of vinegar, white, apple cider, etc?

Agricultural vinegar works best - it's much stronger than household vinegar (20% acetic acid rather than 5%).  You can use regular vinegar (cheap white vinegar is fine) but it won't be nearly as effective.  Depending on where you use it, you can mix it with salt, which is also a non-specific plant killer - the best method is ot boil the vinegar, hypersaturate it with salt (stir in as much salt as you can while it's hot) and then pour it on the undesirable plants.  However, you need to realize that straight vinegar, of any strength, with or without salt, is a non-specific plant killer - it will kill anything enough of it lands on - so don't use it unless you can isolate what you're trying to kill from whatever you're not trying to kill, including any run-off.  There is no residual - it won't stay in the soil unless you use enough salt to totally destroy the dirt's ability to support plant life - but it is safe for chilldren and pets.

I've tried white vinegar. My experience is that it did seem to kill the weeds, but they kept coming back. I use Roundup because they don't come back when I use it. But I'd prefer something natural.

Jill

 If you can't find agricultural vinegar, take the grocery store kind and boil it down to at least half volume, or 10% acidity. 5% isn't strong enough to do the job completely. Be careful where you put it, though!