Blender's keymap is famous for being different, and since the 2.8 series it is also consistent: the same key does the same thing in every editor where it makes sense. Nearly all of the shortcuts below are single letters with the mouse over the 3D viewport, so the first habit to build is keeping the cursor in the viewport before pressing anything.
View 9
Selection 5
Basic Tools 9
Editing 8
Animation 5
G, R, S and the axis trick
G grabs (moves), R rotates and S scales the selection, and each of them starts an interactive operation rather than switching tools — you press the key, move the mouse, and click or press Enter to confirm. Typing an axis letter afterwards constrains the operation, so G then Z moves only vertically, and typing a number sets an exact amount. Shift + D duplicates and immediately enters grab mode so the copy can be placed, while Alt + D makes a linked duplicate that shares mesh data. X deletes with a confirmation menu.
Edit mode is where the modelling keys live
Tab toggles between Object and Edit mode on the active object, and Ctrl + Tab opens the pie menu with every mode. Inside Edit mode, E extrudes the selection, I insets a face, Ctrl + R starts a loop cut that follows the mouse until you click, K is the knife, and F fills selected edges or vertices with a face. P separates the selection into a new object and Ctrl + J joins objects back together. Ctrl + A applies transforms, which you need to do before modifiers and exports behave predictably.
Selection and views
A selects everything and Alt + A deselects — note that since 2.8, pressing A again no longer toggles. B and C start box and circle select, and Ctrl + I inverts. The numpad keys are views: Numpad 1, Numpad 3 and Numpad 7 for front, side and top, Numpad 0 for the camera, and Numpad . to frame the selection. On a laptop without a numpad, enable "Emulate Numpad" in Preferences and the number row takes over.
Animation
I in the viewport inserts a keyframe for the active object (a different action from the inset it performs in Edit mode) and Alt + I deletes one. Space plays and pauses, Left/Right steps a frame and Shift + Left/Right jumps to the first or last frame of the range.
Frequently asked questions
Why does pressing A twice not deselect anymore?
Since Blender 2.8, A only selects all. Use Alt + A to deselect all, or double-tap A if you enable the legacy option in Preferences › Keymap.
How do I use the view shortcuts on a laptop without a numpad?
Enable Emulate Numpad in Preferences › Input. The number row then works as the numpad views.
What does Ctrl + A (Apply) do and when do I need it?
It bakes the object's location, rotation or scale into the mesh data. Apply scale before adding modifiers such as Bevel or Array, or their results will be distorted.
Why does I do different things?
Over the viewport in Object mode it inserts a keyframe; in Edit mode with faces selected it insets them. The mode decides.