Movement

Keystroke(s)	Meaning
h, j, k, l	The big four: left, down, up, right (←, ↓, ↑, →)
w, W, b, B	Forward one word, back one word
e, E	end of current word
(, )	Beginning of previous sentence; end of next sentence (doesn't always work correctly!)
{, }	Beginning of previous paragraph; end of next pararaph
0, ^	First position, first character
$	End of line
+, -	First character of next or previous line
H, M, L	Top line of screen, middle line, last line
^F, ^B	Forward one screen, back one screen
^D, ^U	Down half a screen, up half a screen
z RET	Position current line at top of screen
/something	Search forward for something
?something	Reverse search for something
/ RET	Repeat last search forward
? RET	Position current line in middle of screen
^G	Reports status line (including the current line's number)
^G	Reports status line (including the current line's number)
G n RET, :n RET	Go to absolute line n
G	Go to last line
mx	Mark current as x
'x	Go to mark x

Editing

Keystroke(s)	Meaning
i	Insert text
a	Append text (very useful at the end of line!)
o, O	"Open" a new line immediately below current, "open" a new line immediately above current
r	Change one character
cw	Change a word from the current point
cc	Reinitialize the current line
C	Change from current point to end of line
R	Overwrite mode
x	Delete the current character
dw	Delete word
dd	Delete current line
D	Delete from current character to end of line
p	Put back at current
P	Put back at previous (much more useful!)
"np	Go back in delete history n items for P
yw	Copy word (use p,P to retrieve)
yy	Copy line (use p,P to retrieve)
"ayy	Copy line into buffer a
"aP	Paste line from buffer a
:%s/something/otherthing/g	Replace something with otherthing throughout the current file
u, U	Undo; restore line (very useful!)