Even if you've got 100 servers, you are probably not going to be allocated your own block of IP addresses. You would have to justify needing at least a couple of hundred addresses and you also have to have the network connectivity to make it work. Your DSL or cable modem doesn't qualify as the proper network connectivity.
That's one of a few reasons the DNS system exists. That and it's a lot easier to remember www.webmasterworld.com than 184.108.40.206.
Here's how the system works:
1) You register a domain name
2) You set up DNS entries on a DNS server for that domain name
3) You set up the DNS server information at the domain registrar
4) John Smith decides to go to www.example.com
5) His computer asks his ISP's DNS server for the IP address for www.example.com
6) The ISP's DNS server asks the root DNS servers which DNS servers are authoritative for example.com
7) The ISP's DNS server asks the authoritative DNS servers what the IP address is for www.example.com
8) The ISP's DNS server gives that response back to John Smith's computer
9) John Smith's computer requests the web page from your server (by IP address)
There are two routes you can take to get this to work:
1) Register your own domain name
This isn't that expensive. It will cost you $7-40 per year depending on who you register the name with.
I'm going to suggest namecheap.com. The price is pretty good and they've got their own DNS servers, so you can set up the DNS information directly and not have to worry about getting someone to provide DNS services. (I'm assuming that this machine is in your house and not hosted by a web hosting company.)
If your IP address changes very rarely (fixed IP or a cable modem), you can set up an A record with the IP address and be done. If the IP address changes, you update the A record.
If your IP address changes frequently, you can use NameCheap's dynamic DNS client. You run a program on your computer that watches for the IP address to change. Whenever the IP address changes, it sends a request to the NameCheap server to update the address in the A record.
Either way, when someone requests www.imawebdude.com, they go get the IP address from the DNS server and find your computer. If the IP address changes, they get the new IP address when they request it from the DNS server.
Pretty nifty, eh?
2) If you don't want to register a domain, you can get a subdomain from someone like dyndns.org. After you set up an account with them, you can register something like mydomain.dyndns.org and the process works exactly the same way. This option is free.