Do you know that by pressing Ctrl + H you can toggle show/hide selected path. This is useful to see your artwork without the selected paths obscuring your view, especially useful when coloring your objects.
Do you know that by pressing Ctrl + U you can toggle on and off the smart guides feature. Smart guides are very useful if you want to move objects around and line it up against another object. But can be very annoying to have it on all the time. So Ctrl + U is a quick way to turn it on and off.
When clicking around using the pen tool, before you let go of your left mouse button, you can shift the point by holding the space bar and moving your mouse. Very convenient and handy for that extra precision when drawing your object out. This is unique for Illustrator, it doesn't work for Photoshop.
If you want to draw a rectangular/square box with exact "swiss precision" pixel dimensions, don't click and drag. Just click on the rectangular box icon and click once on your work area. A pop up will appear and you can type in the exact width and height. Handy if you're old and your hands are shaky.