Windows 7 Keyboard Shortcuts

[Lecter]

Win+Home: Clear all but the active window
Win+Space: All windows become transparent so you can see through to the desktop
Win+Up arrow: Maximize the active window
Win+Down arrow: Minimize the window/Restore the window if it's maximized
Win+Left/Right arrows: Dock the window to each side of the monitor (If you've got dual monitors, adding Shift to the mix (e.g., Win+Shift+Right arrow) will move the window to the adjacent monitor)
Win+T: Focus and scroll through items on the taskbar
Win+P: Adjust presentation settings for your display
Win+(+/-): Zoom in/out
Shift+Click a taskbar item: Open a new instance of that application

[Lecter]

Brandon Paddock (a Microsoft employee working on Windows 7) lists the new Windows 7 hotkeys, including ones that'll make the new taskbar easier to use.

General
Win+Up: Maximize
Win+Down: Restore/Minimize
Win+Left: Snap to left
Win+Right: Snap to right
Win+Shift+Up: Maximize vertically
Win+Shift+Left: Jump to left monitor
Win+Shift+Right: Jump to right monitor
Win+Home: Minimize/Restore all other windows
Win+T: Focus the first taskbar entry—pressing again will cycle through them, you can can arrow around
Win+Shift+T: Cycles backwards
Win+Space: Peek at the desktop
Win+G: Bring gadgets to the top of the Z-order
Win+P: External display options (mirror, extend desktop, etc.)
Win+X: Mobility Center (same as Vista, but still handy!)
Win+B: Focuses the System Tray icons
Win++ (or) Win+- (Win + the plus or minus key): Zoom in or out

Win+#: (# = a number key) Launches a new instance of the application in the N'th slot on the taskbar, or opens a already existing instance
Example: Win+1 launches first pinned app, Win+2 launches second, etc.
Win+Shift+#: Launches a new instance of the N'th pinned application
Win+Ctrl+#: Cycles through open windows of the N'th pinned application
Win+Alt+#: Opens the Jump List of the N'th pinned application

Explorer
Alt+P: Show/hide Preview Pane
Ctrl+Shift+N: Creates a new folder in Windows Explorer
Alt+Up: Goes up a folder level in Windows Explorer
Shift+Right-Click on a file: Adds Copy as Path, which copies the path of a file to the clipboard
Shift+Right-Click on a file: Adds extra hidden items to the Send To menu
Shift+Right-Click on a folder: Adds Command Prompt Here, which lets you easily open a command prompt in that folder

Taskbar Modifiers
Shift + Click on icon: Open a new instance
Middle click on icon: Open a new instance
Ctrl + Shift + Click on icon: Open a new instance with Admin privileges
Shift + Right-click on icon: Show window menu (Restore/Minimize/Move/etc.)
Note: Normally you can just right-click on the window thumbnail to get this menu
Shift + Right-click on grouped icon: Menu with Restore All/Minimize All/Close All, etc.
Ctrl + Click on grouped icon: Cycle between the windows (or tabs) in the group

[Lecter]

There is a built-in shortcut key in Windows 7 that opens up the Jump Lists for the first 9 taskbar icons—you can use Win+1, Win+2, etc. to cycle between open windows on the taskbar or launch an application, you can use the Win+Alt+1 shortcut key combination to open up the Jump List for the icon in that position in the taskbar.

[Lecter]

You can also interact with windows by dragging them with the mouse:

Drag window to the top: Maximize
Drag window left/right: Dock the window to fill half of the screen
Shake window back/forth: Minimize everything but the current window
Double-click top window edge (cursor will change to double arrow): Maximize window vertically