At no time has there ever been a Linux kernel release with no local root exploits. There have been periods of uncertainty when we didn't know the exact exploit but we always find out eventually. Keep this in mind whenever you think about Linux security.
That said, Linux users do have an unwarranted confidence in the security of the operating system. The kernel developers actually don't care that much about security--but because it was designed with some level of sanity, most installations are headless, and the non-headless installations aren't used by very many people, it has been able to tout some apparently obvious superiority to e.g. Windows (which isn't really the case post-Vista, when Microsoft had enough of being a punching bag.) Same thing goes for Mac--a whole lot of confidence, but not a lot to back it up. Curiously, a lot more Mac malware has shown up after they gained considerable market share.
There is no security in this world, only opportunity.
Careful. I'm not making a "Linux vs. Windows" argument here. I'm making a Linux desktop vs. any other computing environment argument. Not all computing environments are equally exposed to attacks. It is for instance much more annoying to exploit iOS vulnerabilities than it is to pivot from user "nobody" to root on an Ubuntu desktop system.
That these two environments aren't comparable --- one is a heavily-locked down and simplified computing environment and one is a general purpose desktop operating system --- is exactly my point.
I totally agree. It wouldn't be fair to compare Ubuntu to Chrome OS either. (My response was aimed more at thrownaway2424's comment, and I didn't mean to give the impression that everything is equally vulnerable, just that most software has exploitable bugs that may or may not be known.)