Chrome: If you work with multiple Chrome instances, especially if they're spread out across multiple monitors, you probably do quite a lot of tab moving. Speed things up with QuickShift, a shortcut-based Chrome tab mover.
While Chrome offers smooth drag-and-drop shifting of tabs between windows, if you're doing a lot of tab moving across multiple instances you waste a lot of time mousing about. QuickShift for Chrome is a lightweight extension that enables tab shifting via keyboard shortcuts. You can use CTRL+ALT+ left/right arrow to move tabs back and forth between windows to the left and right of the current Chrome instance. If no instance exists to the right or left, QuickShift creates a new window and populates it with the tab you're moving. In addition to slinging tabs between instances, you can also use CTRL+ALT+[1-9]to move the tab within its current window to the numbered position in the tab bar.
QuickShift for Chrome is free and works wherever Chrome does. For more tab-wrangling Chrome extensions make sure to check out previously reviewed TabRocket to send Chrome tabs between computers, Tab Sugar for some visual tab management that's heavy on the eye candy, and Move Your Tabs to slap your tabs on the side of the browser window for widescreen-friendly space management.