Property 'json' does not exist on type 'Object'

UPDATE: for rxjs > v5.5

As mentioned in some of the comments and other answers, by default the HttpClient deserializes the content of a response into an object. Some of its methods allow passing a generic type argument in order to duck-type the result. Thats why there is no json() method anymore.

import {throwError} from 'rxjs';
import {catchError, map} from 'rxjs/operators';

export interface Order {
  // Properties
}

interface ResponseOrders {
  results: Order[];
}

@Injectable()
export class FooService {
 ctor(private http: HttpClient){}

 fetch(startIndex: number, limit: number): Observable<Order[]> {
    let params = new HttpParams();
    params = params.set('startIndex',startIndex.toString()).set('limit',limit.toString());
    // base URL should not have ? in it at the en
    return this.http.get<ResponseOrders >(this.baseUrl,{
       params
    }).pipe(
       map(res => res.results || []),
       catchError(error => _throwError(error.message || error))
    );
} 

Notice that you could easily transform the returned Observable to a Promise by simply invoking toPromise().

ORIGINAL ANSWER:

In your case, you can

Assumming that your backend returns something like:

{results: [{},{}]}

in JSON format, where every {} is a serialized object, you would need the following:

// Somewhere in your src folder

export interface Order {
  // Properties
}

import { HttpClient, HttpParams } from '@angular/common/http';
import { Observable } from 'rxjs/Observable';
import 'rxjs/add/operator/catch';
import 'rxjs/add/operator/map';

import { Order } from 'somewhere_in_src';    

@Injectable()
export class FooService {
 ctor(private http: HttpClient){}

 fetch(startIndex: number, limit: number): Observable<Order[]> {
    let params = new HttpParams();
    params = params.set('startIndex',startIndex.toString()).set('limit',limit.toString());
    // base URL should not have ? in it at the en
    return this.http.get(this.baseUrl,{
       params
    })
    .map(res => res.results as Order[] || []); 
   // in case that the property results in the res POJO doesnt exist (res.results returns null) then return empty array ([])
  }
} 

I removed the catch section, as this could be archived through a HTTP interceptor. Check the docs. As example:

https://gist.github.com/jotatoledo/765c7f6d8a755613cafca97e83313b90

And to consume you just need to call it like:

// In some component for example
this.fooService.fetch(...).subscribe(data => ...); // data is Order[]

For future visitors: In the new HttpClient (Angular 4.3+), the response object is JSON by default, so you don't need to do response.json().data anymore. Just use response directly.

Example (modified from the official documentation):

import { HttpClient } from '@angular/common/http';

@Component(...)
export class YourComponent implements OnInit {

  // Inject HttpClient into your component or service.
  constructor(private http: HttpClient) {}

  ngOnInit(): void {
    this.http.get('https://api.github.com/users')
        .subscribe(response => console.log(response));
  }
}

Don't forget to import it and include the module under imports in your project's app.module.ts:

...
import { HttpClientModule } from '@angular/common/http';

@NgModule({
  imports: [
    BrowserModule,
    // Include it under 'imports' in your application module after BrowserModule.
    HttpClientModule,
    ...
  ],
  ...