It has been said that a good mechanic can generally do a bolt up to about 80% of it's yield stress just by feel. I think that's probably true. Much of the enthusiasm for torquing everythig to a particular value just comes from using robotised production lines. You need to set the robot to "something". Also in the current litigious climate, it's the first thing any compensation lawyer would ask in the case of a failure and subsequent lawsuit. Pretty much everyone knows that as long as the bolt was "tight" it will have been fine, but it dosn't take much for a lawyer to "cast reasonable doubt" and then the manufacturer is in trouble! If you specify a numerical value, then you can have a quality control check point that can audit that value on the production line, and that will allow a box to be ticked. If you just specify "tight" then the guy doing the QC check has to make a subjective decision as to whether it was or not.
Not just head bolts but fasteners round a big gasket (like a sump, cam cover or timing chain cover) benefit from being torqued because often, long before the bolt is in any danger of snapping or the thread in any danger of stripping) you can overdo them and cause the gasket to leak by making the cover "bulge" between fasteners. With big, gasketed joints like these, often "less is more" when it comes to tightening the fasteners. Also things like whel bolts, where over-tightenng (and you've got to be a really insensitive gorilla to do it!) can cause the hub and disc to distort and cause an effect like "warped brake disc".
Like Peter, I rarely use a torque wrench on my own cars, but I can see the reasons why it's a good idea!