My issue was the same as reported by DBDAN. I was in the process of writing a stored procedure when I needed to do a quick query for something different. I used the same window I was working in -- as I always do -- but this time that incomplete (and thus incorrect) code to create a stored procedure prevented IntelliSense from working. When I commented it out IntelliSense worked again. Un-comment, and IntelliSense failed. Re-comment, IntelliSense worked. And I also found, when un-commented, that IntelliSense did work in the window above the incomplete/incorrect code, but not below it.

Thanks Rikard Askelöf and DBDAN!