Cursor movement
h		move left
j		move down
k		move up
l		move right
w		jump by start of words (punctuation considered words)
W		jump by words (spaces separate words)
e		jump to end of words (punctuation considered words)
E		jump to end of words (no punctuation)
b		jump backward by words (punctuation considered words)
B		jump backward by words (no punctuation)
0		(zero) start of line
^		first non-blank character of line
$		end of line
G		Go To command (prefix with number
		Note:	Prefix a cursor movement command with a number to repeat it. For example, 4j moves down 4 lines.

Insert Mode	Inserting/Appending text
i		start insert mode at cursor
I		insert at the beginning of the line
a		append after the cursor
A		append at the end of the line
o		open (append) blank line below current line (no need to press return)
O		open blank line above current line
ea		append at end of word
Esc		exit insert mode

Editing
r		replace a single character (does not use insert mode)
J		join line below to the current one
cc		change (replace) an entire line
cw		change (replace) to the end of word
c$		change (replace) to the end of line
s		delete character at cursor and subsitute text
S		delete line at cursor and substitute text (same as cc)
xp		transpose two letters (delete and paste, technically)
u		undo
.		repeat last command
Marking text (visual mode)
v		start visual mode, mark lines, then do command (such as y-yank)
V		start Linewise visual mode
o		move to other end of marked area
Ctrl+v	start visual block mode
O		move to Other corner of block
aw		mark a word
ab		a () block (with braces)
aB		a {} block (with brackets)
ib		inner () block
iB		inner {} block
Esc		exit visual mode

Visual commands
>		shift right
<		shift left
y		yank (copy) marked text
d		delete marked text
~		switch case

Cut and Paste
yy		yank (copy) a line
2yy		yank 2 lines
yw		yank word
y$		yank to end of line
p		put (paste) the clipboard after cursor
P		put (paste) before cursor
dd		delete (cut) a line
dw		delete (cut) the current word
x		delete (cut) current character

Exiting
:w		write (save) the file, but don't exit
:wq		write (save) and quit
:q		quit (fails if anything has changed)
:q!		quit and throw away changes

Search/Replace
/pattern	search for pattern
?pattern	search backward for pattern
n		repeat search in same direction
N		repeat search in opposite direction
:%s/old/new/g	replace all old with new throughout file
:%s/old/new/gc	replace all old with new throughout file with confirmations

Working with multiple files
:e filename	Edit a file in a new buffer
:bnext		go to next buffer
(or :bn)
:bprev		go to previous buffer
(of :bp)
:bd			delete a buffer (close a file)
:sp filename	Open a file in a new buffer and split window
ctrl+ws		Split windows
ctrl+ww		switch between windows
ctrl+wq		Quit a window
ctrl+wv		Split windows vertically