smontgom. You beat me to it.
haha IP addresses do NOT start from 0.0.0.0 to 255.255.255.255. In fact, IP addresses do not even start with 0 or 255 OR end with 0 or 255. 255 in hex would equal FF, and in IP terms that would register as a 1 or "broadcast". 0 would of course be zero or in IP terms "the network". This all because of the mask 255.255.255.0. (telephone companies also do NOT assign numbers from 200-0000 to 999-9999, I used to work for a telephone company but I won't even get started on that). Ethernet addresses are assigned by the Internet Standards Organization (ISO) more or less. I forget which branch actually handles the first 24bit MAC (actually the first 2 bits). Local IP addresses are assigned according to your MAC address. Your MAC address is a UNIQUE, 48bit set of numbers (hex) attached to your Network Card or Integrated Interface. The first 24bits are assigned by the manufacturer of that Network Card. The first 2bits of the first 24bits are assigned by the ISO to specific manufactures. Are you following?
ISPs are given a set of IP ranges in whatever class they are in. A, B, or C (D and E you don't need to worry about). Each of these classes have a range which you can determine by your mask. 255.255.255.0 is class C. Now when you take both of these sets of ranges you can see how unique an IP can get. If you're running on a router or switch or server of some sort then it possible and actually quite common for 2 people to have the same IP addresses, HOWEVER, you do not connect to THAT IP. You would be connecting to a WAN IP address. The IP address given to you by your ISP. Most IP addresses (localy) are 192.168.2.x or 192.168.1.x but you obviously cannot connect to these addresses since they are local IP addresses. But there ARE ways of obtaining the IP from someone reguardless of direct connections or file transfers. Hackers will use port sniffers or service scanners to check for open ports or unprotected services. IP addresses (WAN) can easily be obtained this way. If you're trying to obtain an IP from someone you're simply chatting to you could run Peeking programs such as EtherPeek (if you're willing to spend the big bucks). But this would also require you to know how to break apart individual packets and read HEX fluently. All in all, if this kind of stuff interests you so much... take Networking classes and obtain a degree.
And DO NOT try to obtain an IP for revenge. IP addresses are traceable... even on wireless connections. Anything you do can be scanned, monitored, and traced to the very spot you are sitting.