For debugging it is very helpful to start C:\Program Files (x86)\Android\android-studio\bin\studio.bat.
That points out what is wrong. In my case I had to update my JDK_HOME environment variable to point to the currient installation.
From the android documentation (this part was published after I wrote my answer):
Known issue: On some Windows systems, the launcher script does not find where Java is installed. If you encounter this problem, you need to set an environment variable indicating the correct location.
Select Start menu > Computer > System Properties > Advanced System Properties. Then open Advanced tab > Environment Variables and add a new system variable JAVA_HOME that points to your JDK folder, for example C:\Program Files\Java\jdk1.7.0_21.
