For me it depends. When I'm learning a new technology stack or API I'll typically break out Reflector, and my usage of it goes up.
For instance I recently started working with the Commerce Server 2007 API. I found much of the documentation around the Profile System incomplete or lacking in sufficient detail for my curiousity. So I broke out reflector, and used it to inspect the Commerce Membership Provider implementation (not to mention the implementation of the native asp.net sql membership provider).
Inspecting the code helped me much better understand how and why the membership providers work the way they do, versus just relying on what the documentation said.
I was then able to go on and implement a custom membership provider for commerce server that I believe made up for some of the limitations of the stock commerce server membership provider. Granted my implementation was not looking to be as generic and feature rich, as my goal was to establish "standard" setup and configuration of the commerce user profile for my company.
So when I was initially working with commerce server, I spent probably 20% of my time in reflector. Now that I have better understanding I rarely use it to inspect commerce server at least.
Secondly, when i first started working with asp.net ajax and the ajax web control toolkit. The toolkit is open source. I spend a fair amount of time in the control toolkit code initially, the documentation was ok, but the samples were very weak. Dividing into the source code helped me better understand use its various web controls to their full capacity. It also helped me better and more deeply learn how to work with the asp.net ajax javascript libraries. Initially I spent about probably 10% of my time in the source code of the toolkit.
Day to day how much time do I spend using reflector? Not that much, depends on the project and if the technology involved is familiar or new.