Angular CLI version 9 (used to create Angular 9 projects) now picks up style from schematics instead of styleext. Use the command like this:
ng config schematics.@schematics/angular:component.style scss
and the resulting angular.json shall look like this

"schematics": {
   "@schematics/angular:component": {
      "style": "scss"
    }
  }

Other possible solutions & explanations:

To create a new project with angular CLI with sass support, try this:

ng new My_New_Project --style=scss 

You can also use --style=sass & if you don't know the difference, read this short & easy article and if you still don't know, just go with scss & keep learning.

If you have an angular 5 project, use this command to update the config for your project.

ng set defaults.styleExt scss

For Latest Versions

For Angular 6 to set new style on existing project with CLI:

ng config schematics.@schematics/angular:component.styleext scss

Or Directly into angular.json:

"schematics": {
      "@schematics/angular:component": {
      "styleext": "scss"
    }
}

ng set --global defaults.styleExt=scss is deprecated since ng6. You will get this message:

get/set have been deprecated in favor of the config command

You should use:

ng config schematics.@schematics/angular:component '{ styleext: "scss"}'

If you want to target a specific project (replace {project} with your project's name):

ng config projects.{project}.schematics.@schematics/angular:component '{ styleext: "scss"}'

For Angular 9.0 and above, update the "schematics":{} object in angular.json file like this:

"schematics": {
  "@schematics/angular:component": {
    "style": "scss"
  },

  // Angular 13 may contain this as well; NOT related
  "@schematics/angular:application": {
    ...
  }
},

Angular-CLI is the recommended method and is the standard in the Angular 2+ community.

Crete a new project with SCSS

ng new My-New-Project --style=sass

Convert an existing project (CLI less than v6)

ng set defaults.styleExt scss

(must rename all .css files manually with this approach, don't forget to rename in your component files)

Convert an existing project (CLI greater than v6)

1. rename all CSS files to SCSS and update components that reference them.
2. add the following to the "schematics" key of angular.json (usually line 11):

"@schematics/angular:component": { "styleext": "sass" }

As of 3/10/2019, Anguar dropped the support of sass. No mater what option you passed to --style when running ng new, you always get .scss files generated. It's a shame that sass support was dropped without any explanation.

The following should work in an angular CLI 6 project. I.e if you are getting:

get/set have been deprecated in favor of the config command.

npm install node-sass --save-dev

Then (making sure you change the project name)

ng config projects.YourPorjectName.schematics.@schematics/angular:component.styleext sass

To get your default project name use:

ng config defaultProject

However: If you have migrated your project from <6 up to angular 6 there is a good chance that the config wont be there. In which case you might get:

Invalid JSON character: "s" at 0:0

Therefore a manual editing of angular.json will be required.

You will want it to look something like this (taking note of the styleex property):

...
"projects": {
    "Sassy": {
      "root": "",
      "sourceRoot": "src",
      "projectType": "application",
      "prefix": "app",
      "schematics": {
        "@schematics/angular:component": {
          "styleext": "scss"
        }
      }
...

Seems like an overly complex schema to me. ¯_(ツ)_/¯

You will now have to go and change all your css/less files to be scss and update any references in components etc, but you should be good to go.

TL;DR

Quick note: In Angular 9 & onwards, styleext is renamed to style

Angular 9 & 9+
While creating a new project:
ng new my-proj --style=scss

For an existing one:
ng schematics.@schematics/angular:component.style scss

For Angular 2 - Angular 8:
For an existing project:
ng config schematics.@schematics/angular:component.styleext scss

Detailed answer

Angular 9 & 9+ :

Via Angular CLI

ng config schematics.@schematics/angular:component.style scss

Directly in the angular.json:

"schematics": {
   "@schematics/angular:component": {
   "style": "scss"
   }
}

For older versions

Via the Angular CLI:

ng config schematics.@schematics/angular:component.styleext scss

Directly in the angular.json:

note: lookup angular-cli.json for versions older than 6. For version 6 & 6+ the file has been renamed to angular.json

"schematics": {
   "@schematics/angular:component": {
   "styleext": "scss"
   }
 }

Note: Original SO answer can be found here

CSS Preprocessor integration Angular CLI supports all major CSS preprocessors:

To use these preprocessors simply add the file to your component's styleUrls:

@Component({
  selector: 'app-root',
  templateUrl: './app.component.html',
  styleUrls: ['./app.component.scss']
})
export class AppComponent {
  title = 'app works!';
}

When generating a new project you can also define which extension you want for style files:

ng new sassy-project --style=sass

Or set the default style on an existing project:

ng config schematics.@schematics/angular:component.styleext scss

note: @schematics/angular is the default schematic for the Angular CLI

Style strings added to the @Component.styles array must be written in CSS because the CLI cannot apply a pre-processor to inline styles.

Based on angular documentation https://github.com/angular/angular-cli/wiki/stories-css-preprocessors

For Angular 12 update angular.json with:

"schematics": {
   "@schematics/angular:component": {
      "style": "scss"
    }
  }

and:

"build": {
  "options": {
    ...
    "inlineStyleLanguage": "scss"
  }
}

"test": {
  "options": {
    ...
    "inlineStyleLanguage": "scss"
  }
}

Step1. Install bulma package using npm

npm install --save bulma

Step2. Open angular.json and update following code

...
 "styles": [
 "node_modules/bulma/css/bulma.css",
 "src/styles.scss"
 ],
...

That's it.

To easily expose Bulma’s tools, add stylePreprocessorOptions to angular.json.

...
 "styles": [
 "src/styles.scss",
 "node_modules/bulma/css/bulma.css"
  ],
 "stylePreprocessorOptions": {
 "includePaths": [
    "node_modules",
    "node_modules/bulma/sass/utilities"
 ]
},
...

BULMA + ANGULAR 6

DO NOT USE SASS OR ANGULAR's EMBEDDED CSS SYSTEM!!

I cannot stress this enough. The people at Angular did not understand basic cascading style sheet systems as when you use both these technologies - as with this angular.json setting - the compiler stuffs all your CSS into Javascript modules then spits them out into the head of your HTML pages as embedded CSS that breaks and confuses cascade orders and disables native CSS import cascades.

For that reason, I recommend you REMOVE ALL STYLE REFERENCES FROM "ANGULAR.JSON", then add them back into your "index.html" manually as links like this:

<link href="styles/styles.css" rel="stylesheet" />

You now have a fully functioning, cascading CSS system that's fully cached in your browser over many refreshes without ECMAScripted circus tricks, saving huge amounts of bandwidth, increasing CSS overall management in static files, and full control over your cascade order minus the clunky embedded CSS injected into the head of all your web pages which Angular tries to do.

SASS isn't even necessary when you understand how to manage cascades in basic CSS files. Large sites with complex CSS can be very simple to manage for those that bother to learn cascade orders using a handful of linked CSS files.