By rough analogy with Turing-completeness and NP-completeness, I think we have entered a malware-complete age. By this, I mean that it's pretty difficult for an individual to have confidence that their machine does not have malware.
Looking at all the NSA revelations, plus various other stories of state-sponsored hacking, it's clear that there are huge resources available. If a large government wants you hacked, you'll be hacked. They will have known exploits for pretty much all the software you use - look at how long Heartbleed was about, for example, to get an idea of what they probably know about.
Computer viruses really entered the public awareness in the early '90s, and the Morris worm was in '88. Reflections on Trusting Trust was '83, and I'm sure there's plenty more before that, so there's plenty of history to malware, but I think it's only recently that it's become impossible to reasonably harden a general-purpose computer.
The thing is that there's now so huge an attack surface. If you're got gigabytes of RAM and terabytes of disk, it's easy to hide things. You can have user-mode spyware, root kits, things that hide in virtualisation. You can probably do fun things at the microcode level, like a malicious version of the F00F bug fix. There's the BIOS. Everything will have a microcontroller and firmware in, keyboards, mice, SD memory cards, hard disks. All able to be subverted. Your internet router probably has a back door.
I was thinking to myself, 'What is the most useful computer I could feel confident working with, to feel my data would be properly safe, against government-style foes?'. Assuming they can't access my stuff physically (ha ha), and ignoring Tempest, etc., it would probably be a late '90s PC with an open source operating system, disconnected from networking and all external storage I/O disabled. And you know what? I still wouldn't trust it.