public class MyActivity extends Activity {
  @Override
  public void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    WebView webview = new WebView(this);
    setContentView(webview);
    webview.loadUrl([MY URL]);
  }
  ..
}

CookieManager.getInstance().setAcceptCookie(true);

CookieManager.getInstance().setAcceptThirdPartyCookies(webView, true);

CookieSyncManager.createInstance(context)

CookieSyncManager.getInstance().startSync()

CookieSyncManager.getInstance().stopSync()

CookieSyncManager.getInstance().sync()

// use cookies to remember a logged in status
CookieSyncManager.createInstance(this);
CookieSyncManager.getInstance().startSync();
WebView webview = new WebView(this);
webview.getSettings().setJavaScriptEnabled(true);
setContentView(webview);
webview.loadUrl([MY URL]);

WebView webview = new WebView(this);
  webview.setWebViewClient(new WebViewClient() {
      @Override
      public boolean shouldOverrideUrlLoading(WebView view, String url)
      {
        view.loadUrl(url); //this is controversial - see comments and other answers
        return true;
      }
    });
  setContentView(webview);
  webview.loadUrl([MY URL]);

CookieManager.getInstance().setAcceptCookie(true);

CookieSyncManager.createInstance(this);
CookieManager cookieManager = CookieManager.getInstance();
cookieManager.removeAllCookie();
cookieManager.setAcceptCookie(true);