According to the report, 48 percent of users aren't running the latest, patched versions.
"This is not because Java is more difficult to patch, but the program has a high market share and a lot of the users neglect to patch the program, even though a patch is available," said Kasper Lingaard, the company's director of research and security.
There were 119 new vulnerabilities identified in Java over the past year and the software is installed on 65 percent of computers, according to the report.
The report collects information from millions of users of Secunia's patch management software, so may actually be undercounting these vulnerabilities.
"Users who have sufficient security awareness to install a patch management program can reasonably be assumed to have high security standards, compared to the average PC user," said Lingaard.
Apple Quicktime 7.x was in second place, with 14 new vulnerabilities, 57 percent penetration on desktops, and 44 percent unpatched.
Other applications on the top-ten list included Adobe Reader 10.x and 11.x, Microsoft .NET framework 2.x, 3.x, and 4.x, VLC Media Player 2.x, Internet Explorer 11.x and Microsoft XML Core Services 3.x.
Internet Explorer had the most vulnerabilities, at 248, and this was an increase over last year, when it didn't even make the top ten list.
"It's too early to conclude whether it's a bad or good sign," Lingaard said. For example, the increase in vulnerabilities could be because Microsoft is paying more attention to browser security, and it could be the result of the Internet Explorer 11 Preview Bug Bounty.
According to the report, 47 percent of vulnerabilities last year were due to Microsoft programs, 47 percent to third-party software, and the remaining 6 percent to the operating system.
The average computer had 76 different programs installed from 27 different vendors -- 41 percent of which were Microsoft programs, and the remaining 59 percent were from other vendors.
The third-party programs were about twice as likely to be unpatched -- 11.6 percent to 5.2 percent -- because each one has a different update process. Microsoft programs, however, can be updated through one mechanism.
In addition, 12.9 percent of users have an unpatched operating system, and 5.7 percent of applications don't have patches available because they've passed their end-of-life date.
For example, Adobe Flash Player 15 is an end-of-life program -- but is installed on 73 percent of PCs.
While the report only covers private computers, the data could apply to some business environments as well, Lingaard said.
"There is no reason to assume that the patch status is any different on corporate end user devices that are not rigorously controlled and patched by the IT team," he said.
In addition to the US, Secunia also released individual reports for eleven European countries, Saudi Arabia, Australia, and New Zealand, and the results varied slightly by geography.
For example, the percentage of unpatched operating system ranged from a low of 8.1 percent in the Netherlands to a high of 17.2 percent in Saudi Arabia.