- When one wants to discover new Web content (using the same query)
- When one is doing research on a particular topic
- When one is looking for some rare information
Check out screenshots of the SERPs of Google, Yahoo, Bing and Ask.com for the query time pass activities. It's clear that in this situation, having four different engines helps. For similar reasons, using multiple search engines (sometimes) helps in case (2) and (3).
And that's why I'm sad at the impending folding of Yahoo Search into Bing. It was good to have Yahoo Search as an independent player...