Details
Note blocks play a musical note when hit or when powered by redstone. Redstone current only causes the note to play once, even if it is a continuous current. A note block must have at least one block of air above it to play a sound. Notes can be heard up to 48 blocks away.
As of the official release of Minecraft, note blocks will play when next to a powered block.
Each time a note block plays a note, a note particle will fly out of the top, with the color depending on the pitch (but not the instrument).
A Note Block being triggered and playing a note.
Right clicking increases the note pitch up a half step, with a total of two full octaves being available to play. The range of notes span from F#3 to F#5. After reaching the highest note, right clicking again resets it back to F#3, as does breaking the block and picking it back up.