Why can't I ssh or ping my brand new Amazon EC2 instance?

Apparently the default firewall is locked down, even though it doesn't look like it. Go to "Security Groups" on the left-hand pane of the AWS console, and select the "default" group. There are already entries for all TCP,UDP, and ICMP from a Source of "default group".

For a new entry at the bottom, select "SSH" from the "Connection Method" dropdown. The Source will default to "0.0.0.0/0" instead of "default group". Click "Save" over on the right and now it should respond when you try to SSH in.

If you want to ping it, create a similar new entry with protocol "ICMP", leaving the Connection Method as "Custom..."