The addresses are issued based on MAC address (aka "Burned-In Address," "Hardware Address," Ethernet Address" and others)
The address is issued for the duration of a "lease time;" Until the least expires or until you have a new MAC address (i.e., new router, different host) you will continue to get that IP address.
I've had the same cable address for years, though my DSL address changes a couple times a week. It's up to the ISP (as mentioned) some give long-term leases, some are pretty short (to reduce the number of folks trying to set up servers).
Most people *like* having the same address for a long time.
Good Luck
Scott