Can looking at pornography in your own home on your computer lead to criminal charges? Like most aspects of law the answer is not so simple, but the short answer is YES. However, looking at adult pornography in your own home is not what can get you into trouble. It is child pornography that is illegal.
There are two aspects of so called cyber porn that involve children. One is the issue of children or minors looking at porn on the internet. Many courts have ruled that software is available to protect minors from inadvertently viewing pornography online. Adult pornography, whether on the internet or elsewhere is considered a protected part of free speech and therefore cannot be prohibited. Groups have tried to prevent internet porn on the basis that children could easily be subjected to porn on the internet but consistently courts have considered protective software preferable to an abridgment to the first amendment right to free speech.
The second issue is that of the actual depiction of children in pornography. Courts have ruled that child pornography is not protected by the first amendment and is therefore subject to criminal penalties. It can be a crime to knowingly posses, sell, receive, send or transmit child pornography through the internet.