Navigation:
h - Left
j - Down
k - Up
l - Right

Advanced Navigation:
w - Goto beginning of word(Forward)
b - Goto beginning of word(Backward)
e - Goto End of Word
G - Goto end of file
gg - Goto start of file
#g - Goto Line # (Ctrl+G shows line number)
% - Goto start/end of matching paranthesis like {},[],()

Modes: (ESC returns to Normal Mode)
v - Visual Mode
i - Insert Mode (Current position)
a - Insert Mode (Append)
A - Insert Mode (End of Line)
o - Append New Line and Insert Mode
O - Prepend New Line and Insert Mode

General: (Append ! to force action ignoring errors)
:w - Write to file
:r - Insert from file
:q - Quit

Clipboard:
d - Cut
y - Copy
p - Paste

Deleting:
dw - Delete Word
d$ - Delete till End of Line
d^ - Delete till Start of Line
dd - Delete entire Line

Undo & Redo:
u - Undo
Ctrl+R - Redo

Replace:
r - Replace single character
R - Replace until exited to normal mode
ce - Edit till end of word

Search:
/ - Forward Search
? - Backward Search
n - Next Occurence
N - Previous Occurence

Find and Replace:
:s/old/new - Replace 'old' with 'new'
Append /g to replace all occurence in the current line
Append /gc to confirm before replacing each occurence
Use :%s to perform Find and Replace on whole file
Use :1,3s to perform Find and Replace between Line 1 and 3

Shell Commands:
:!{cmd} - Executes {cmd}