I use Spaces to organize the task I'm pursing. In that vein, I often will have a browser window on each Space, with open tabs relevant to that task that Space is used for.
For example, Space 1 is for Work. So in addition to work applications, I have a browser window open with tabs relevant to work. Space 2 is for Photography. And Space 3 is for just general browsing and social networking, etc.
I am easily able to put a different browser window into each space. The problem is that when I restart the computer, all windows appear in the first Space!
My browser is Chrome, and perhaps this is an issue I need to take up with the Chrome team. Or is this a bug in OS X Lion?