When you buy a domain from GoDaddy (or other registrars), the typical purchase lasts 1 year from the purchase date, with automatic renewal. But you can register or renew domains for up to 10 years! Whenever you buy a new domain from GoDaddy, you may see an "expiring items" screen before check-out, telling you that "you have x domains expiring soon". Review the expiration dates for each near-expired domain, and decide whether to renew or not (by default, domains auto-renew year to year, but you can disable auto-renewal).
To check the expiration date for a domain you already own, which you registered with GoDaddy, log into your account. If you just logged in, you may see a list of products: if Domains is showing -it should be listed first- click on the Manage button on the right. Otherwise, click on My Account (top right corner of the page), and select "Manage My Domains" on the left.
GoDaddy will now list all domains currently registered and unexpired, sorted alphabetically (domains starting with a number are shown before the letter "a"). Click on the "Expires" column header, as shown on the screenshot.
Your domain are now listed starting with the ones expiring soonest: the expiration date is in red for domains that expire within the next 2.5 months. On the right of the nameservers column, you'll see a green checkmark for each domain set to automatically renew (with GoDaddy) before it expires. If you want to transfer the domain or cancel it, make sure to take care ahead of time: domains transfers can take up to two weeks (mostly because of red tape!)
Bonus Tip:
To check when a current domain registration expires, whether you own it or not, and whether it is registered with GoDaddy or not, type the domain name in the text box below and click Check. you'll see the "Expires on" date near the top.