How to disable automatically adding a closing curly brace or bracket insertion in VS Code?

Question

For new versions of vscode:

"editor.autoClosingBrackets": "never"

You can also do this in a language-specific way by

"[javascript]": {
    "editor.autoClosingBrackets": "never"
}

"always", "languageDefined", and "beforeWhitespace" are the new additional options.
vscode curly braces settings

[Previous, now inaccurate, setting.]

// Controls if the editor should automatically close brackets after opening them

"editor.autoClosingBrackets": false,