The following websites offer tactical puzzles and/or the facilities to play chess on-line. Some features are accesssible free of charge.

•   Chess Kids (for kids!)
  
• LiChess: Learn & Play On Line
•  Chess.com
• ChessOS: play chess online
• Chess Tactics Server: improve tactical awareness
• Chess Tempo (free Tactics Server)

Sites useful for learning to play or improving your chess. Some are entirely free, others are free at beginner levels.

Basic:

• Chess Kids (interactive lessons!) Ideal for young kids.
• Chess Corner
• Learn to Play Chess
• LiChess: Learn & Play On Line
• Chess24.com   (Learn chess with GM Viswanathan Anand )

Intermediate:

• From Beginner to Chess expert in 12 steps  [a guide for improvement]
• Exeter Chess Club [free source of tutorial materials for all levels]
• St Louis Chess Club - youtube instructional videos