Definitely 'The Invisible Man'. The story follows a man who becomes invisible through scientific means but then faces all kinds of problems. It's a great exploration of the human psyche when given extraordinary power.
Sure. 'The War of the Worlds' is a must - read. It's about Martians invading Earth. The description of the alien technology and the panic it causes is really exciting.
His 'The Time Machine' is excellent. It's about a man who travels through time. It gives a very interesting view of how different classes might evolve in the future. There are the Eloi and the Morlocks, which are very different from each other, and it makes you wonder about the direction of human development.