I work in a university, and I've actually been monitoring an extreme and increasing number of hacking attempts against our public-facing site recently--on the order of 150 malicious requests per day, and this directed at a fairly small university. Many attempts were very sophisticated and targeted at known vulnerabilities in our specific CMS, and even specific components and plugins within our CMS.
If we hadn't beefed up our security lately, our server would have been compromised as well. As it stands, we've been monitoring and blacklisting IP addresses at the rate of about 10 per day, mostly from China, though there's been a frightening number of attempts from other universities and US-based hosting companies as well.
Hopefully The Times' revelation will slow down the frantic attempts to compromise our server as well... Could just be wishful thinking on my part, though.