How do I configure my browsers not to save passwords for specific websites? There are certain web sites whose passwords I don't want saved, for security reasons. I want to type them in manually whenever needed.

How do I configure Safari, Chrome and Firefox on Mavericks to not save passwords for these web sites, and not to ask me?

I don't want my browsers to ask me whether to remember the password for these web sites, because I can (and have) selected Yes without thinking, say when I'm in a hurry.
Since you have multiple questions here, I would attempt to answer one of them:

In case of Firefox:

Open the permissions manager

in the address bar type following about:permissions and hit enter

In the new window select the web site to work on and choose the settings.



To further customize a specific web site (fine tune) click on the small Icon in front of that website address. In the new pop up window you can highly customize what that web site can and can not do.