Nanab berry

I use them on low level pidgey/rattata/etc.. to increase the chance on the first catch bonus.

When you get it, then throw away.

I've never used one, but I read on a different site that a Nanab berry prevents the Mon form actually running away?? It may escape the catch,but not run away. I didn't trust this when I read it.
I keep exactly 10 of them in my bag. Any more than that and I toss them.

There is a huge difference. With the Nanab berry, there is a cute little image of the berry next to the Pokemon before you throw the ball. This increases your chance of getting the munchies.

If used first, you can use it with one of the other berries. I use them in combination with the pineapples, just because you want every throw to count.

They would be useless if you couldn't stack the other berries on top of them

Nanab berries are useless.

You want to stockpile Pinap berries for double candy events. Razzberries are also useless if you know how to do the ultraball, curveball great throw or higher combo.

I think Niantic will realize they're useless soon.
I keep some of them just in case they change Nanab to make Pokémon drop twice as much stardust.

You're in a nest and you want to mass farm a certain pokemon and you don't have much time. Toss this on every encounter to greatly reduce the probability of pokemon movements happening and you can aim in peace and save balls. The last thing you want is for those hard-to-catch nest pokemons to bat away your ultra ball 5 times in a row.

You took the question right out my head?? NOPE throw all away. Need space for the new berry.

I occasionally throw at ladybugs or other "jumpy" pokemon that I don't care if I catch or not, and not going to waste a different berry or anything other than a Pokeball.
I've used the double-candy berries either on low-CP pidgey (for evolution spam) or low-CP Dratini - great to get 6 dratini candy with 1 ultraball!