How do I clear the log in Xcode 4? (It seems that in Xcode 3, this required customizing the toolbar, which is no longer possible...)
To which log are you referring? The debugger/run log for the current session can be cleared using the Clear button on its top bar, but all sessions are stored in the Log Navigator.
The stored logs from past run/build/whatever sessions are stored as part of your "derived data" for each project. To view this, open the Organizer window and select the Projects tab. Select the project in question from the list on the left, then where it shows the "derived data" folder, click the arrow to the right of the path to see it in Finder. You can trim the logs in the Logs subfolder manually if you wish (keeping more recent logs) or simply click the Delete... button to the far right of the path in the Organizer window. Doing this will wipe out its logs, its index, and its build output all in one go.