In the latest version of Angular

1. Import HttpClientModule and HttpClientJsonpModule modules in your app module's definition file

    import {
        HttpClientModule,
        HttpClientJsonpModule
    } from '@angular/common/http';
   
    @NgModule({
    declarations: [
        //... List of components that you need.
    ],
    imports: [
        HttpClientModule,
        HttpClientJsonpModule,
        //...
    ],
    providers: [
        //...
    ],
    bootstrap: [AppComponent]
    })
   

2. Inject http and map rxjs operator into your service:

    import {Injectable} from '@angular/core';
    import {HttpClient} from '@angular/http';
    import 'rxjs/add/operator/map';
   
    @Injectable()
    export class MegaSuperService {
       constructor(private _http: HttpClient) {}
    }
   

3. Make JSONP requests in the following way:

    // inside your service
    this._http.jsonp('/api/get', 'callback').map(data => {
    // Do stuff.
    });
   

In Angular version 2 - version 4.3

1. Import JSONP module in your app module's definition file:

    import {JsonpModule} from '@angular/http';
   
    @NgModule({
    declarations: [
        //... List of components that you need.
    ],
    imports: [
        JsonpModule,
        //...
    ],
    providers: [
        //...
    ],
    bootstrap: [AppComponent]
    })
   

2. Inject jsonp service and map rxjs operator into your service:

    import {Injectable} from '@angular/core';
    import {Jsonp} from '@angular/http';
    import 'rxjs/add/operator/map';
   
    @Injectable()
    export class MegaSuperService {
       constructor(private _jsonp: Jsonp) {}
    }
   

3. Make requests using "JSONP_CALLBACK" as a callback property:

    // inside your service
    this._jsonp.get('/api/get?callback=JSONP_CALLBACK').map(data => {
    // Do stuff.
    });
   

In Angular 4.3 and up you should use HttpClientModule because the JsonpModule is deprecated.

1. Import HttpClientModule and HttpClientJsonpModule into your module.
2. Inject HttpClient into your service.
3. Pass the callback key as the second argument for the jsonp method.

app.module.ts

import { BrowserModule } from '@angular/platform-browser';
import { NgModule } from '@angular/core';
// Import relevant http modules
import { HttpClientModule, HttpClientJsonpModule } from '@angular/common/http';

import { AppComponent } from './app.component';

import { ExampleService } from './example.service';

@NgModule({
  declarations: [
    AppComponent
  ],
  imports: [
    BrowserModule,
    // Import relevant http modules
    HttpClientModule,
    HttpClientJsonpModule
  ],
  providers: [ExampleService],
  bootstrap: [AppComponent]
})
export class AppModule { }

example.service.ts

import { Injectable } from '@angular/core';
// Import HttpClient class
import { HttpClient } from '@angular/common/http';

@Injectable()
export class ExampleService {

  // Inject HttpClient class
  constructor(private http: HttpClient) { }

  getData() {
    const url = "https://archive.org/index.php?output=json&callback=archive";

    // Pass the key for your callback (in this case 'callback')
    // as the second argument to the jsonp method
    return this.http.jsonp(url, 'callback');
  }
}

If this endpoint is jsonp-compliant, you can use the following. You need to find out the parameter to use to provide the jsonp callback. In the code below, I call it c.

After having registered JSONP_PROVIDERS when calling the bootstrap function:

import {bootstrap} from 'angular2/platform/browser'
import {JSONP_PROVIDERS} from 'angular2/http'
import {AppComponent} from './app.component'

bootstrap(AppComponent, [ JSONP_PROVIDERS ]);

You can then execute your request using an instance of the Jsonp class you injected from constructor:

import {Component} from 'angular2/core';
import {Jsonp} from 'angular2/http';

@Component({
  selector: 'my-app',
  template: `
    <div>
      Result: {{result | json}}
    </div>
  `
})
export class AppComponent {
  constructor(jsonp:Jsonp) {
    var url = 'https://accounts.google.com/logout&c=JSONP_CALLBACK';
    jsonp.request(url, { method: 'Get' })
     .subscribe((res) => {
       (...)
     });
  }
}

See this question for more details:

• I need to do a http request to a mail chimp subscription list via a component post