I updated Eclipse with the new SDK tools (rev. 23), but now when Eclipse starts I receive the error:
This Android SDK requires Android Developer Toolk
None of the other answers worked for me using the ADT bundle published on developer.android.com.
I ended up downloading the latest version of Eclipse (not the ADT bundle) and then installing the ADT plugin via menu Help → Install new software → entering https://dl-ssl.google.com/android/eclipse
(mentioned by @RED_).
I also had to update my workspace to point to my previous workspace, and most things seemed to be restored.
On a side note: This seems like a good time to migrate to Android Studio...