Neuromancer was just the start of the Sprawl trilogy, so you should certainly go on to read Count Zero and Mona Lisa Overdrive, not to mention the stories in Burning Chrome, which tell us yet more about this future of jacked-in cyber jockeys and street samurai, simstim and emerging machine intelligence. You simply can't understand cyberpunk, or anything that happened in science fiction afterwards, without these books. Note that while these books take place in the same 'world' they are unique stories and as such you can read Neuromancer (or the other loosely connected books) as stand alones.
Gibson has recently returned to science fiction with a powerful new novel, The Peripheral, in which people riding shotgun on an immersive game in the run-down near future end up witnessing a murder in the more distant future, and get caught in a time-travelling mystery of escalating violence and ever-increasing mystery. It can be hard going at first, but boy is it worth keeping on with the book.
If Neuromancer got the ball rolling with cyberpunk, there were an awful lot of great writers who quickly joined him. So if this sets you on fire, you absolutely must go on to read Schismatrix Plus by Bruce Sterling, the novel and stories set in his Shaper/Mechanist universe, a future in which humanity is divided between those who go in for genetic modification of the body, the Shapers, and those who prefer mechanical augmentation, the Mechanists. This is the point where cyberpunk started to mutate into stories of post-humanity.
Then there's Pat Cadigan, especially Synners and Fools, both of which won the Arthur C. Clarke Award, making her the first person to win the award twice. These are dramatic stories of human/machine interface, and the way it affects our awareness of reality.
For more specific CYBERPUNK book recommendations, make sure you look at our 'Top 25 Best Cyberpunk Books list' and our Guide to the Cyberpunk Genre.