Serious certification authorities use heavy procedures. At the core, the CA key will be stored in a Hardware Security Module; but that's only part of the thing. The CA itself must be physically protected, which includes proactive and retrospective measures.
Proactive measures are about preventing attacks from succeeding. For instance, the CA will be stored in a vault, with steel doors and guards. The machines themselves are locked, with several padlocks, and nobody holds more than one padlock key. Physical security is of paramount importance; the HSM is only the deepest layer.
Retrospective measures are about recovering after an incident. The HSM will log all signatures. The machine is under 24/7 video surveillance, with off-site recording. These measures are about knowing what has happened (if you prefer, knowing a priori that, should a problem occur, we will be able to analyze it a posteriori). For instance, if "illegal" certificates have been emitted but the complete list of such certificates can be rebuilt, then recovery is as "easy" as revoking the offending certificates.
For extra recovery, the CA is often split into a long-lived root CA which is kept offline, and a short-lived intermediate CA. Both machines are in the cage and bunker; the root CA is never connected to a network. The root CA is physically accessed, with dual control (at least two people together, and video recording) on a regular basis, to emit the certificate for the intermediate CA, and the CRL. This allows revoking an intermediate CA if it got thoroughly hacked (to the point that its private key was stolen, or the list of fraudulently emitted certificates cannot be rebuilt).
Initial setup of a serious root CA involves a Key Ceremony with herds of auditors with prying eyes, and a formalism which would not have been scorned by a Chinese Emperor from the Song dynasty. No amount of auditing can guarantee the absence of vulnerabilities; however, that kind of ceremony can be used to know what was done, to show that security issues have been thought about, and, come what may, to identify the culprit if trouble arises. I have been involved in several such ceremonies; they really are a big "security theater" but have merits beyond the mere display of activities: they force people to have written procedures for everything.
The question is now: are existing CA really serious, in the way described above ? In my experience, they mostly are. If the CA has anything to do with VISA or MasterCard, then you can be sure that HSM, steel and ill-tempered pitbulls are part of the installation; VISA and MasterCard are about money and take it very seriously.
For the CA which are included in Web browsers and operating systems, the browser or OS vendor tends to require a lot of insurance. There again, this is about money; but the insurance company will then require all the physical measures and accounting and auditing. Formally, this will use certifications like WebTrust.
This is true even for infamous CA like DigiNotar or Comodo: note that while they got hacked and fake certificates were issued, the said certificates are known and were revoked (and Microsoft added them to a list of "forbidden certificates" which can be seen as a kind of "revoked, and we really mean it" -- software must go out of his way to accept them nonetheless).
The "weak" CA are mostly the State-controlled root CA. Microsoft can refuse to include a root key from a private venture, if Microsoft feels that enough insurance has not been provided (they want to be sure that the CA is financially robust, so that operations can be maintained); I know of a bank with millions of customers who tried to get their root key included in Windows, and were dismissed on the basis that they were "too small". However, Microsoft is much weaker against official CA from sovereign states; if they want to do business in country X, they cannot really afford to reject the root CA key from government X. Unfortunately, not all governments are "serious" when it comes to protecting their CA keys...