Do I need a second RAID controller for fault-tolerance?

In a 'single box high availability' design then yes, you'd want a second controller, ideally on a second bus too. But this kind of approach has given way to a cheaper design based around clustering where one box failure doesn't stop service. So it depends on if you plan to use a clustered environment or rely on a single box. Even if your answer is the latter having dual controllers may be seen as adding extra complexity and maybe being overkill.

edit - based on your comment about using ESXi on your other question I'd have to say that its clustering is fabulous, we have many 32-way clusters that work brilliantly.

A second RAID controller which is actively used is not for redundancy. Only if it is a cold-stand-by controller where you switch all your disks to when the first one dies. Then you have redundancy (for the controller). But beware of doing so, as posted here.

So the RAID is for redundancy of disks leading to a single point of failure at the controller. Having a second (unused) controller may solve this as you could switch all the disk to the new one. If this works depends on other factors...

I'm no native speaker, but for me "fault-tolerance" is something different than "redundancy". Can some English speaker help me out here?