Yes!! The same U2F YubiKey can be used with any number of services and there is no practical limit to the U2F-secured services the Security Key and other U2F-certified YubiKeys can be associated with. (To see a list of the YubiKeys you can use, see our comparison page.)
During the registration process, the key pairs are generated on the device (secure element) but the key pairs are not stored on the YubiKeys. Instead, the key pair (public key and encrypted private key) is stored by each relying party/service that initiated the registration. Therefore, this approach allows for an unlimited number of services to be associated with the U2F-certified YubiKeys.
This means the same U2F-certified YubiKey you use for Gmail or Google Apps can be used with your other U2F-enabled accounts. To see where else you can use your U2F-certified YubiKey, see our FIDO U2F page.