Google-maps – How to show traffic and other layers in the new Google Maps

The directions method in Benj's answer didn't work for me anymore. The following query string parameters seemed to do it for me:

https://maps.google.com/?lci=transit_comp

You can find parameters in use for the current view by clicking on the Link button on the left side.

To answer the question regarding changing the default settings in the web app, I can't seem to find a way to change the default layers.

According to The New Google Maps, Now Available (May 17, 2013)

"My Places" is not part of the new Google Maps interface. Click the "options" icon in the black navigation bar, select "My Places" and you'll go back to the old interface. It's a trick that lets you temporarily switch to the old interface. You can also click "classic maps".

However you can still access your "My Places" by going directly to Google Maps - My Places which will contain all of your old maps (which are still editable).

You can also use Google Maps Engine Lite to create and view custom Google Maps.