Here are some great keyboard shortcuts that will help you to use your Mac more efficiently:

See key or legend at the end for unfamiliar keys.

Commands (work in most applications):
⌘C – copy
⌘X – cut
⌘V – paste
⌘Z – undo
⌘⇧Z – redo
⌘B – bold
⌘I – italic/oblique
⌘U – underline
⌘P – print
⌘O – open
⌘R – refresh (chiefly for browsers)
⌘⇧R – hard refresh (most browsers—will redownload page assets, too)
⌘W – close window
⌘⇧W – close all windows
⌘A – select all
⌘S – save
⌘⇧S – save as…
⌘F – find on page/in document (browsers/word processor)
⌘N – new document/thing
⌘[space] – invoke Spotlight (computer-wide search)
⌘⇧3 – screen shot from selection, saved to disk (desktop by default)
⌘⌃⇧3 – screen shot from selection, saved to pasteboard/clipboard
⌘⇧4 – screen shot from selection, saved to disk
⌘⌃⇧4 – screen shot from selection, saved to pasteboard
⌘⇧4,˽ – screen shot of window, saved to disk
⌘⌃⇧4,˽ – screen shot of window, saved to pasteboard

System Commands:
⌘⇥ – rotate through open applications
⌘` – rotate through windows within present application
⌃↑ – invoke Mission Control
⌃→ and ⌃← – move back and forth between desktops
⌃↓ – see windows open within application
⌘⌥⎋ – invoke (open) “Force Quit Application” dialog
⌃⇧⏏ – lock/sleep computer (smaller and newer keyboards often lack the eject [⏏] button)
⌘⌥D – display/hide dock

Unix-y Commands:
⌃A – move cursor to beginning of line (of text)
⌃E – move cursor to end of line

Controls:
⇧⌥ [volume down] – move volume down by quarter steps for more granular control
⇧⌥ [volume up] – move volume up by quarter steps …
⇧⌥ [increase screen brightness] – brighten screen by quarter steps …
⇧⌥ [decrease screen brightness] – dim screen by quarter steps …

Special Characters:
⌥1 – ¡ · ⇧⌥1 – ⁄
⌥2 – ™ · ⇧⌥2 – €
⌥3 – £ · ⇧⌥3 – ‹
⌥4 – ¢ · ⇧⌥4 – ›
⌥5 – ∞ · ⇧⌥5 – fi
⌥6 – § · ⇧⌥6 – fl
⌥7 – ¶ · ⇧⌥7 – ‡
⌥8 – • · ⇧⌥8 – °
⌥9 – ª · ⇧⌥9 – ·
⌥0 – º · ⇧⌥0 – ‚
⌥- – – · ⇧⌥- – —
⌥= – ≠ · ⇧⌥= – ±
⌥, – ≤
⌥. – ≥
⌥; – …
⌥’ – æ
⌥[ – “ · ⇧⌥[ – ”
⌥] – ‘ · ⇧⌥] – ’
⌥\ – « · ⇧⌥\ – »
⌥? – ÷ · ⇧⌥? – ¿
⌥r – ®
⌥t – †
⌥g – ©
⌥k – ˚ · ⇧⌥k – 

Accents:
n · ⌥n,n – ñ, ⌥n,⇧n – Ñ, ⌥n,a – ã, etc.
u · ⌥u,u – ü, ⌥u,⇧u – Ü, ⌥u,o – ö, etc.
i · ⌥i,i – î, etc.
e · ⌥e,e – é, etc.

Key:
⌘ – cmd (command)
⇧ – shift
⌃ – ctrl (control)
⌥ – option or alt (alternate)
⏏ – eject
⎋ – escape
⌦ – delete
⌫ – delete (backspace)
⇥ – tab
˽ – space