New service updated to use the HttpClientModule and RxJS v5.5.x:
import { Injectable }                    from '@angular/core';
import { HttpClient, HttpErrorResponse } from '@angular/common/http';
import { Observable }                    from 'rxjs/Observable';
import { catchError, tap }               from 'rxjs/operators';
import { SomeClassOrInterface}           from './interfaces';
import 'rxjs/add/observable/throw';
@Injectable() 
export class MyService {
    url = 'http://my_url';
    constructor(private _http:HttpClient) {}
    private handleError(operation: String) {
        return (err: any) => {
            let errMsg = `error in ${operation}() retrieving ${this.url}`;
            console.log(`${errMsg}:`, err)
            if(err instanceof HttpErrorResponse) {
                // you could extract more info about the error if you want, e.g.:
                console.log(`status: ${err.status}, ${err.statusText}`);
                // errMsg = ...
            }
            return Observable.throw(errMsg);
        }
    }
    // public API
    public getData() : Observable<SomeClassOrInterface> {
        // HttpClient.get() returns the body of the response as an untyped JSON object.
        // We specify the type as SomeClassOrInterfaceto get a typed result.
        return this._http.get<SomeClassOrInterface>(this.url)
            .pipe(
                tap(data => console.log('server data:', data)), 
                catchError(this.handleError('getData'))
            );
    }
Old service, which uses the deprecated HttpModule:
import {Injectable}              from 'angular2/core';
import {Http, Response, Request} from 'angular2/http';
import {Observable}              from 'rxjs/Observable';
import 'rxjs/add/observable/throw';
//import 'rxjs/Rx';  // use this line if you want to be lazy, otherwise:
import 'rxjs/add/operator/map';
import 'rxjs/add/operator/do';  // debug
import 'rxjs/add/operator/catch';
@Injectable()
export class MyService {
    constructor(private _http:Http) {}
    private _serverError(err: any) {
        console.log('sever error:', err);  // debug
        if(err instanceof Response) {
          return Observable.throw(err.json().error || 'backend server error');
          // if you're using lite-server, use the following line
          // instead of the line above:
          //return Observable.throw(err.text() || 'backend server error');
        }
        return Observable.throw(err || 'backend server error');
    }
    private _request = new Request({
        method: "GET",
        // change url to "./data/data.junk" to generate an error
        url: "./data/data.json"
    });
    // public API
    public getData() {
        return this._http.request(this._request)
          // modify file data.json to contain invalid JSON to have .json() raise an error
          .map(res => res.json())  // could raise an error if invalid JSON
          .do(data => console.log('server data:', data))  // debug
          .catch(this._serverError);
    }
}
I use .do() (now .tap()) for debugging.  
When there is a server error, the body of the Response object I get from the server I'm using (lite-server) contains just text, hence the reason I use err.text() above rather than err.json().error.  You may need to adjust that line for your server.
If res.json() raises an error because it could not parse the JSON data, _serverError will not get a Response object, hence the reason for the instanceof check.
In this plunker, change url to ./data/data.junk to generate an error.
Users of either service should have code that can handle the error:
@Component({
    selector: 'my-app',
    template: '<div>{{data}}</div> 
       <div>{{errorMsg}}</div>`
})
export class AppComponent {
    errorMsg: string;
    constructor(private _myService: MyService ) {}
    ngOnInit() {
        this._myService.getData()
            .subscribe(
                data => this.data = data,
                err  => this.errorMsg = <any>err
            );
    }
}