Depending on who is looking into your IP, a variety of things can happen. Here are some facts that may help put an IP into perspective.
An IP address is an attribute for the TCP/IP protocol, thus is a software setting, not hardware.
Most people have a wired or wireless router in their home, so the public or externally facing IP address is usually bound to the router, while some kind of class C network is running inside their home. (Class C networks generally use the first two octets, 192.168)
The most commons types of IPs are Static or Dynamic. Static IPs are usually defined on several network service by a network administrator (DNS, Firewalls, Routing Tables, and more). Some might say that a network with static IPs is more secure. Static IPs allow you to use system hosts files as a solid work around for DNS, as well as prevents the need for DHCP. DNS servers can be exploited to find out what systems are on a network. DHCP servers can as well. Additionally DHCP and DNS servers can be hit with DoS attacks, preventing your users from being able to access network resources.
Dynamic IPs are usually maintained by a DHCP server. Which will automatically issue an IP to a system when it is connected. Newer Windows 7/8/2008R2 domain policies can allow you to configure DHCP with advanced security options, so that only a PC registered with the Active Directory domain can connect to the network. This prevents someone from walking into your office building and plugging a home laptop into any open port, getting an IP address and start probing.
One analogy I like to use when explaining an IP versus Ports. Is that one should think of your IP as your mailing address, and each port as a person at the residence. You could have 3 people living in one house, that all share the same address. Similarly, you can have 3 programs running on your computer, that are all sharing the same IP address. Programs know which packet of data is theirs, based on the port that is used for delivery. This is why having a basic firewall and the latest security patches are so crucial. There are many ports that Windows, linux and Mac listen to regularly without your consent. When hackers discover a technique to access your computer through some port or service, it's not always shared with the vendor and could leave you vulnerable for several days before a fix is available to download through updates.
It is also important to make sure you are running updated firmware within your router at home. As I mentioned earlier, your public IP address is generally assigned to your router. So if you use Netgear, Belkin, Linksys, etc. You will want to make sure those devices are secure as well.
Once you go upstream from your house you start to leave the realm of software networking and would get more involved with hardware networking. This is usally provided by an ISP and can range from Coaxial Copper Cabling, Fiber optic cabling, wireless radio (verizon? satellites), and more. At this point we are talking about multiplexing, timing, circuits, relays, exchanges and even telephony. Most of the technology started out being used for telephones. (http://en.wikipedia....branch_exchange)
These days, most of these systems are maintained through remote computer systems. Generally they are secured and only available to employees of the company that provide your connection or "circuit". Because of this, these companies generally have databases which contain your name, address, billing information and so on.
So, when you are doing something illegal with your internet connection, realize that once your IP is logged. With a warrant from a judge (depending on your country and laws), your information can be retrieved by a 3rd party with only your IP address. In theory, a 'hacker' could also hack your ISPs data systems and steal your private information. However, this is highly illegal and not even practical. Your common anime fan with the screen name Hax0r4Lif3 won't be able to accomplish this.
Last, there are some services that provide 'public' information about IPs and security vulnerabilities. The metasploit framework is a system that was developed to provide a way to perform 'penetration' testing. That is, a way for you to attempt to hack your own systems. http://en.wikipedia....asploit_Project there are a few distributions of linux that take advantage of this framework to provide you with tools to do your own testing. Backtrack 5 is an older linux distro that provided a lot of these tools. Backtrack has since become more professional and is used by a lot of security folks as 'Kali LInux'.
http://en.wikipedia.org/wiki/BackTrack
Another public service are the 'whois' lookup services that allow you to find out public information about a domain name or IP. Personally I like the network solution's who is lookup. http://www.networkso...whois/index.jsp
If you want to know your 'public' IP, which could change regularly if your ISP is using DHCP rather than static, you can go to google and just type, 'what is my ip'. then do a who is lookup and see what kind of information is available. You will instantly see that there is a phone number and email for an administrator. This is the person that can probably find out where you live pretty easily. There is sometimes an Abuse number available as well, so that you can report spammers and hackers who are attempting to access your computer using their IP.
Not sure why i felt the need to go into this much detail, but it is what it is. Also I typed a lot of this pretty quickly so I may have misspoke on some things. Please feel free to correct me if it helps you sleep tonight.