Where I feel torquing has most value is when you have two bolts clamping the same piece of metal and want even pressure across those two bolts. Think stem bolts, faceplate bolts, and even those little Shimano crank-arm bolts. When a torque wrench isn't handy, I'll pay extra attention to the amount of hand pressure on the multiple bolts involved in, for example, a stem face plate. I try to keep the tightening pressure even across all four.

I will do without a torque wrench if one isn't handy, and will use one when it is convenient. I own three of them, so it's usually convenient unless I'm out somewhere.