You can navigate to the current route with new query params, which will not reload your page, but will update query params.

Something like (in the component):

constructor(private router: Router) { }

public myMethodChangingQueryParams() {
  const queryParams: Params = { myParam: 'myNewValue' };

  this.router.navigate(
    [], 
    {
      relativeTo: activatedRoute,
      queryParams: queryParams, 
      queryParamsHandling: 'merge', // remove to replace all query params by provided
    });
}

Note, that whereas it won't reload the page, it will push a new entry to the browser's history. If you want to replace it in the history instead of adding new value there, you could use { queryParams: queryParams, replaceUrl: true }.

EDIT: As already pointed out in the comments, [] and the relativeTo property was missing in my original example, so it could have changed the route as well, not just query params. The proper this.router.navigate usage will be in this case:

this.router.navigate(
  [], 
  {
    relativeTo: this.activatedRoute,
    queryParams: { myParam: 'myNewValue' },
    queryParamsHandling: 'merge'
  });

Setting the new parameter value to null will remove the param from the URL.

@Radosław Roszkowiak's answer is almost right except that relativeTo: this.route is required as below:

constructor(
    private router: Router,
    private route: ActivatedRoute,
) {}

changeQuery() {
    this.router.navigate(['.'], { relativeTo: this.route, queryParams: { ... }});
}

In Angular 5 you can easily obtain and modify a copy of the urlTree by parsing the current url. This will include query params and fragments.

  let urlTree = this.router.parseUrl(this.router.url);
  urlTree.queryParams['newParamKey'] = 'newValue';

  this.router.navigateByUrl(urlTree); 

The "correct way" to modify a query parameter is probably with the createUrlTree like below which creates a new UrlTree from the current while letting us modify it using NavigationExtras.

import { Router } from '@angular/router';

constructor(private router: Router) { }

appendAQueryParam() {

  const urlTree = this.router.createUrlTree([], {
    queryParams: { newParamKey: 'newValue' },
    queryParamsHandling: "merge",
    preserveFragment: true });

  this.router.navigateByUrl(urlTree); 
}

In order to remove a query parameter this way you can set it to undefined or null.