How to do no-fuss auto-routing with ground planes that works well:

• Group bottom, ground, and bottom layer together.
• Group top, power, and power layer together.
• Lay out your circuit, yadda yadda.
• Run ground traces on the ground layer and power traces on the power layer:
  • Turn off all layers but the ground (or power) layer.
  • Use Ctrl-F on any ground (or power) connection.
  • Use Select/Select all found.
  • Use Connects/Auto-route selected rats.
  • Auto-optimize and miter.
• Turn on the top and bottom layers.
• Route everything else using Connects/Auto-route all rats.
• The Message Log will report that your layout is complete.
• Auto-optimize and miter.
• Select the power and draw a rectangle.
• Select the ground and draw a rectangle.
• This fills-in the ground plane, but you're not done, because you still have the traces.
• Do these steps for both ground and power:
  • Use Ctrl-F on any ground connection (best where the power comes in).
  • While you're there, select the Thermal (THRM) tool and drop a thermal on that connection.
  • Use Select/Select all found
  • Use Select/Rip up selected auto-routed tracks.
  • Use Connects/Optimize rats nest again.
• Use Connects/Auto-route all rats.
• The Message Log will report that your layout is complete.

There's a bunch of steps, but it will work a champ every time, because first routing power and ground ensures that when you flood it with power and ground planes, you'll have full connectivity. The only drawback is that you can get unnecessarily long traces and jumps to the other plane involving extra vias. On a 27 part board, I only spotted two jumps and one derp trace.

All of this is necessary because the auto-router doesn't know that the ground plane will magically disappear when you lay a trace across it.