What a really good question!
If you use a dial-up connection to the internet, then your IP address changes every single time you log on.
If you use an "Always-On" (High-Speed?) connection, then you may keep the same IP address for days, weeks, or even months!
(Even if you re-boot!)
Or, you may even have a "Static" IP address, which always stays the same.
But most sites don't use your IP address to identify you.
Most sites, like hotmail and e-bay, use a small text file called a "Cookie". When you go to their website, they install this small, usually harmless, file onto your comuter called a "Cookie".
When you come back to thier site, they search for their "Cookie" on your computer and, when they find it, they know who you are.
You can disable Cookies in your browser, but many sites will tell you that you must have cookies enabled in your browser to access ther web site.
You can clear your cookies after each web session
(Launch Internet Explorer, then on the top bar, click on "Tools - Internet Options - Delete Cookies - OK)
Then the next time you visit the web sites that use Cookies, they won't know who you are until you tell them by signing on.