Well, there ARE a couple of linux-worms out there, that try to worm themselves in through brute-forcing ssh, or unpatched holes in web-software like forums, but choose good passwords, and auto-update your software and they won't come in...
Dedicated, targeted attacks by someone who knows what he's doing often still are effective...
For the rest, here's a list of things that make linux pretty tough to break into on a large scale:
1: Software is installed pretty much exlusively from a trusted source (the repositories). This makes trojan horses pretty much impossible.
2: All software is auto-updated, making abusing old holes very hard.
3: Everyone can search for holes and contribute patches, before or after the software gets released. This means that you don't have to rely on single vendors for your security, and generally speaking, holes are discovered earlier, and fixed faster. Biggest source of holes on linux? Adobe's flash-plugin...
4: No 2 distro's are alike, deminishing the amount of machines malware can affect.
5: Filesystem-rights, giving proper separation of machine and user, and access-control. Malware can't really do much to affect the machine without additional trouble.
6: Things like AppArmor and SElinux, that limit what individual applications can do, down to the bare minimum of what they need.
7: A general sense in the community that security matters.
8: Not relying on/bothering the user to make or keep its machines secure.
So basically, no trojan horses, quick patching, lots of trouble to make something that's effective, and even if something does get in, it can't do squat...