Save open tabs in Chrome
Solution 1:
Check out the Session Buddy and Session Manager extensions for Chrome.
Solution 2:
If you right-click a tab, there is a "Bookmark All Tabs..." option you can use.
Solution 3:
I know it's already solved, but if you are looking for an extension that works on multiple computers without the need of sending files over via email or such, then take a look at TabCloud. You can't drag and drop items into groups, but doing it by hand still beats every other extension if you rely on syncing your tabs.
Update: I can't recommend Pinboard.in highly enough. It has this feature among several others.
Solution 4:
I recommend OneTab, as it's a great way to maintain URLs persistently until you decide what you want to do with them.