Here are some other puzzle and game applets I've come across:

• The Maze page has mazes which you navigate from a rat's perspective.
• LifeLong Universe: Carnival World - Java Puzzle presents a novel 2-D puzzle.
• The Paint by Numbers Home Page has a series of puzzles where you reconstruct images through logic and deduction.
• The Temple of Alife. This page has several java-based cellular automata games.
• Conway's Game of Life has a very good java implementation of Conway's Life with many classic starting patterns.