There are pros and cons to operating your own Web server.
It really depends what content you want to host--personal or professional--and the kind of Web traffic you want to generate.
First, you really should check with your current cable Internet provider; some providers have prohibitions against individual Web hosting due to the increased bandwidth usage you'll likely incur.
You may also need a slightly more robust computer than what you have now; Dell, for example, sells computers designed to operate as Web servers.
Next, do you feel comfortable providing your own technical support should your Apache server ever crash? And what about criminal hacking? Make sure you include the protection of firewall, antivirus, antispyware, and antispam software and hardware solutions for your new Web server.
Depending on your exact needs, you may find that the increased overhead of providing your own Web hosting service costs you more than you'd pay for someone else to provide that service. See our Web hosting buying guide
for a more complete exploration of this topic.