Yes. I have several email accounts tied into my Gmail.
You want to have a look at the Accounts and Import tab under "Settings". There you can add other email addresses that you own.
Obviously, if it's not Gmail, you'll need to know some other information, like the POP3 and/or IMAP server information (password, port). You'll also need to confirm that you control the address before you can add it to Gmail.
More information at Gmail support.