Android SDK Manager Not Installing Components
Try running Android Studio as an administrator, by right-clicking on the .exe and selecting "Run As Administrator".
Also, some anti-virus programs have been known to interfere with SDK Manager.
I was getting a similar permission issue and SDK Manager could not download and install new components. Error message was (I'm running Android Studio (I/O Preview) 0.2.9)
"Unable to create C:\Program Files (x86)\Android\android-studio\sdk\temp"
Although solution was infact what @william-tate's answer says, I could not run the 'SDK Manager' directly. It fails with message:
Failed to execute tools\android.bat The system cannot find the file specified.
Instead I ran the 'tools\android.bat' as Administrator, which in turn launched SDK Manager with same permissions which fixed the issue.
Hope this helps for someone who faces the issue I faced.