Paul Gorman's Vim cheatsheet (You might also want to peruse my .vimrc at paulgorman.org)

Move to . . .

h, j, k, l character left, down, up, right
0, gm, $ start, midule, end of line
b, w start of word left, right
B, W start of whitespaced word left, right
ge, e end of word left, right
gE, E end of whitespaced word left, right
H, M, L top, midule, bottom of screen
^f, ^b next, previous screen
gg, G start, end of file
`. previous change
`` last jump
^o, ^i older, newer :jump
[ENTER] first non-white char of next line
% matching brace
{, } next, previous empty line
(, ) next, previous sentence
:n line number n

Edit . . .

i a before, after cursor
I A before, after line
o O new line below, above
r replace character
R type over
J join this, next line
~ change character case
u undo
^r redo
U undo current line changes
>>, << indent, de-indent
^n, ^p complete word
^x^l complete line
:changes show changes

Bookmarks

m[a-z] mark here as [a-z]
m[A-Z] same, but GLOBAL
`x go to mark x
'x go to line with mark x
:marks list marks

Cut . . .

x, X next, last character
dd current line
D to end of line
:10,20 d lines 10 through 20
:'x,'y d between mark x and y

Copy & paste

yy copy line
yn copy n lines
[visual] y copy selection
gv re-select visual area
P p paste before, after
:reg show register contents
"x use x for next y/p/d

Files

:e file open file
:e . explore dir
:e sftp://me@example.com/myfile open sftp
:e! revert to saved
:w file save file
:wq save, close
:q! close, don't save

Search . . .

/foo foo forward
?foo foo backward
* next word under cursor
# prev word under cursor
n N again forward, back
:%s/foo/bar/gic replace all, ignore case, confirm each
:s/foo/bar/gI replace all on current line, mind case
:'x,'y s/foo/bar/g replace between marks x and y

Macros

qx record to x
q stop recording
@x execute x

Visual mode

v enter visual mode
^v visual block mode
ggVG select all

Buffers, views, tabs

:ls (or :buffers) list buffers
:bn, :bp next, prev buffer
:bd close buffer
:sp, :vsp split view horizontal, vertical
^w^w move cursor viewport
^w q close viewport
^w -/+/= resize viewport
:tabnew file new tab
gt, gT next, prev tab
:tabc close tab
:tabdo %s/foo/bar do to all tabs
zz, zt, zb view line center, top, bottom

Options

:set number show line numbers
:set nonumber hide line numbers
:set paste autoindent off
:set hlsearch highlight matches
:set syntax=perl set syntax

Miscellaneous

:h quickref help
. repeat last command
g ^g word count
g? rot 13
:ce 80 center line columns
:%! filter filter file
:! filter filter selection
:! sort example of above
:ab lw LongWord Abbreviate LongWord
:una lw unset abbreviation
]s, [s next, last misspelled
zg, zug add to dict, undo add
z= suggest spelling

Use the normal command in Ex mode to execute the macro on multiple/all lines:

Execute the macro stored in register a on lines 5 through 10.

:5,10norm! @a

Execute the macro stored in register a on all lines.

:%norm! @a