The certification authorities (CAs) have provided methods to have your certificates issued and signed using a SHA-2 hashing algorithm. As we move ahead, you will see the CAs changing the default signing algorithm from SHA-1 to SHA-2.
It’d be sound strategy to move all of your certificates to SHA-2 and do some testing. Don’t worry about the operating systems and the browsers as they support SHA-2. But make sure your other applications also support SHA-2. These are the applications that your company has coded or have procured from a third party.
You will also see that the issuing CA will be signed using SHA-2, and so will your CRL and OCSP responses. However, in many cases, you will not see the root certificate signed using SHA-2. Why?
In short, the signature on a root certificate is not verified as the software trusts the root certificate public key directly. A root certificate is self-signed and is not signed by another entity that has been given authority. The root certificate gets authority through the root certificate program managed by the operating system or browser developer.
In a root certificate program, the developer determines a certificate policy that provides the rules with which the CA has to comply. The CA states compliance to the policy through the publication of its Certificate Policy or Certification Practice Statement documents. The CA confirms compliance to these rules by providing third-party audits such as those performed by WebTrust. If the CA meets the certificate policy, then the root is trusted and embedded in the software. As such, verification of trust using the signature is not required.
In Microsoft’s responses to their SHA-1 deprecation policy, they state the following: “The SHA1 deprecation policy does not impact SHA1 root certificates, because Windows relies on other means to validate root certificates besides the signature. But all root CAs are expected to switch to use SHA2 to sign any subordinate CA certificates, CRLs, etc.”
So please do not be concerned if the website you are visiting does not use a SHA-2 signed root certificate.
Updated September 11, 2014: Google is also sun-setting SHA-1, but regarding roots state "Note: SHA-1-based signatures for trusted root certificates are not a problem because TLS clients trust them by their identity, rather than by the signature of their hash."