[SalesForce] use a Lightning Component in the Winter ’16 Lightning Experience

This got bumped up to the top... anyway there is now a way to do this as of Summer '18: Lightning Components that implement lightning:isUrlAddressable. See here: https://developer.salesforce.com/docs/component-library/bundle/lightning:isUrlAddressable/documentation

You can navigate to the URL and pass initial state parameters (including record ID) to get you started.

The one.app is the lightning app that has the sidebars and all the standard salesforce features.

When you create a custom app, you will notice your app has name like myApp.app. This app doesn't get any of the functionalities of the one.app. If you need a sidebar in this app, you would have to implement it yourself.

If you want to have the sidebar, may be you should navigate to a lightning component tab instead of a lightning app?

Of course this only works if the contents of your app can also be contained within a lightning component and added to a lightning component tab.

---EDIT--- Following this example, Here's how you would do it:

var urlEvent = $A.get("e.force:navigateToURL");
     urlEvent.setParams({
      "url": "https://lightningtest-dev-ed.lightning.force.com/one/one.app?source=aloha#eyJjb21wb25lbnREZWYiOiJvbmyI6ImxpZ2h0bmluZ2twcjpuZXN0ZWRDb21wb25lbnRzIn19LCJ0IjoxNDY3MzkwNDY0NzQwfQ%3D%3D"
    });
    urlEvent.fire();