If you want to take your AE chops to the next level, you need to know your shortcuts like the back of your hand. There's a ton of shortcuts and which ones you need to remember depends on your workflow. To get you started, Topher put together this primer which does not cover every shortcut there is so if you have some good ones to share, please do so in the comments and help make this the "Ultimate" Guide to After Effects Keyboard Shortcuts.
The first keyboard shortcuts I ever learned, were the keys to display certain properties. S shows Scale, P shows Position, A shows Anchor Point, R for Rotation, and T for Opacity (T is for Transparency I guess, but it displays Opacity). Consequently, if you press one of these, and then hold down shift and continue to press more keyboard shortcuts, it will display them as well, without getting rid of the previous. This goes for any parameter-displaying keyboard shortcuts we talk about.
I hate having to go to where my toolbar palette is located, so I have made it a point to memorize these keybaord shortcuts to switch my tools instantly: V for Selection Tool, H for Hand Tool, Z for Zoom Tool, W for Rotation Tool (Wotation?), C cycles through the various Camera Tools, as well as the new Unified Camera Tool in AECS4, Y for the Pan Behind Tool (to move your Anchor Point), Q cycles through the shape/mask tools, G cycles through the various Pen Tools, Control+T switches between Vertical and Horizontal Text Tools, Control+B is for the Brush, Clone Stamp, or Eraser Tools, and Control+P is for the Puppet Tool (AECS3 and above). Also keep in mind you can hold the Space Bar or the Scroll Wheel button if you have one on your mouse to enable the Hand Tool as well. Also you can use the Scroll Wheel to zoom in and out in your composition window.
Previewing and Display Shortcuts:
I touched on this in my last article, 11 Frequently Asked Questions about After Effects, with explaining how to RAM preview correctly. Numpad Zero previews Audio and Video, Numpad Period previews only Audio, and Enter previews only Video. Also holding Control+Scrubbing your timeline displays A/V in realtime. Now that's out of the way, here are some more shortcuts to save you some time. Caps Lock will temporarily suspend image updates until you hit it again, Alt-Clicking the Grid and Guide Options or hitting the ' (apostrophe) key will toggle the Title/Action Safe Zones. You can also use the ~ (tilda) key to display the palette your mouse is currenly within the bounds of to make it full screen.
These are going to tell how to move around in your timeline as well as setting work areas easier, and modifying parameters. First off, you can use the B key to set the beginning of your work area and the N key to set the end... great for if you need to RAM preview certain areas. You can select certain layers and hit Control+Alt+B to set your work area to the duration of those layers, or if no layers are selected it will reset the work area to the entire comp. Also to refine that you can use the Page Up and Page Down keys to move frame by frame within the timeline, and adding shift to the mix moves you 10 frames either way. Using Alt+Page Down/Up moves your layer 1 frame or Shift+Alt+Page Down/Up moves it 10 frames. The J and K keys will move you right and left between keyframes, and if you want to make a keyframe Easy Ease, just select it and hit F9. Also to move to the very beginning or end of your comp, hit the Home key or End key. Add Shift to that, and you move to the beginning or end of you Work Area.
Pretty simple concept, but its time consuming to keep going to the File menu time after time. These will help you with constant trips up north. Control+Alt+Shift+T makes a new text layer, Control+Y makes a new solid (Control+Shift+Y modifies your solid settings), Control+Alt+Shift+L makes a new light, Control+Alt+Shift+C makes a new camera, Control+Alt+Shift+Y makes a new Null Object. To add the last effect you used is Control+Alt+Shift+E.. You can make a new composition with Control+N, as well as modify your Composition Settings with Control+K. For duplicating layers you use Control+D, but to split a layer you use Control+Shift+D. To use the Make Movie function (same as sending to Render Queue, but with an Output already generated) is Control+M.
Only If You Have It:
This section is dealing with shortcuts that only deal with things that display if you have them. Such as if you hit the U key, it displays all keyframes, but if there are no keyframes, it shows nothing. You can use this by selecting one layer, or certain layers to show the properties for those layers only. Also, if you have no layers selected, pressing these shortcuts will reveal the parameters for all the layers in the composition. EE reveals all Expressions, RR reveals Time Remapping properties, LL reveals audio Waveform, as well as L reveals parameter to modify the level of volume. MM will show any masks and their properties, as well as F showing just the Mask Feather, M showing just the Mask Shape, and TT just the Mask Opacity. If a layer is 3D you can use AA to show the Material Options, E shows any Effects applied, and UU displays all the modified properties for the layer selected.
File Menu Shortcuts:
This is the stuff that really doesn't have to deal with the design aspect of using After Effects, but it is a really helpful thing to know when you are working on a deadline. For a new project hit Control+Alt+N and to open a project is Control+O. There are few different ways to save too: Regular save is Control+S, to Save As is Control+Shift+S, and to Increment and Save is Control+Alt+Shift+S. Importing files is Control+I and Importing Multiple Files at once is Control+Shift+I. You can also import files by double clicking in the project window, and if you shift select or control select within the import box that pops up, you can select multiple files.
That about does it for this massive roundup of Keyboard Shortcuts. Remember you can change your shortcuts and make them custom by going to Adobe.com and downloading the script from Jeff Almasol, but I would recommend against it. Additionally, you can find some sweet keyboards and keyboard stickers online to make your work area even more awesome than it already was.