Just to add to abrannan's post,
With cable and dsl providers and their DHCP assigned IP's, even when the lease expires, you will only get a new IP IF someone assumes yours. I install a lot of remote building management systems, and we use the cheaper dynamic ip dsl plans, and out of 50+ sites, over the last 3 years only maybe 3 or 4 have actually changed ip's yet!
Its also pretty hard sometimes to get a new IP if you want one. Eg. Telus DSL in Edmonton, my home mail server had a "opps" and got blacklisted by IP, I tried the standard release/renew, changed dsl modems, changed routers, changed Nics, no matter what I did I couldn't get a new IP, so I changed providers. I even tried to contact Telus to ask them to force a change if possible, no go...
sd