How do I set the baseUrl for Angular HttpClient?

Use the new HttpClient Interceptor.

Create a proper injectable that implements HttpInterceptor:

import {Injectable} from '@angular/core';
import {HttpEvent, HttpInterceptor, HttpHandler, HttpRequest} from '@angular/common/http';
import {Observable} from 'rxjs/Observable';

@Injectable()
export class APIInterceptor implements HttpInterceptor {
  intercept(req: HttpRequest<any>, next: HttpHandler): Observable<HttpEvent<any>> {

    const apiReq = req.clone({ url: `your-api-url/${req.url}` });
    return next.handle(apiReq);
  }
}

The HttpInterceptor can clone the request and change it as you wish, in this case I defined a default path for all of the http requests.

Provide the HttpClientModule with the following configurations:

providers: [{
      provide: HTTP_INTERCEPTORS,
      useClass: APIInterceptor,
      multi: true,
    }
  ]

Now all your requests will start with your-api-url/

Based on TheUnreal's very useful answer, the interceptor can be written to get the base url through DI:

@Injectable()
export class BaseUrlInterceptor implements HttpInterceptor {

    constructor(
        @Inject('BASE_API_URL') private baseUrl: string) {
    }

    intercept(request: HttpRequest<any>, next: HttpHandler): Observable<HttpEvent<any>> {

        const apiReq = request.clone({ url: `${this.baseUrl}/${request.url}` });
        return next.handle(apiReq);
    }
}

BASE_API_URL can be provided by the application module:

providers: [
    { provide: "BASE_API_URL", useValue: environment.apiUrl }
]

where environment is the object automatically created by the CLI when generating the project:

export const environment = {
  production: false,
  apiUrl: "..."
};