As a teacher of high school kids who study the quadratic formula in algebra classes, I see all sorts of good reasons to spend time with it. 1. Kids ought to be encouraged to generalize their results at every oportunity. Programmable calculators make this worth their while when they can use their generalization to write a quadratic equation-solving program (I know, there is a dedicated function built in to the TI-83 etc. but it's much nicer for the kids to write their own first - also, the first time their discriminent is negative and they get an error message is a wonderful opportunity for further discussion). 2. The understanding about what it means "to be in the form of", as in, to use the formula, an equation must be in the form of ax^2 + bx + c = 0 is more sophisticated than most of us recognize, and it is essential. 3. I encourage kids to approximate rational values for the roots they get when using the quadratic formula - in their head (i.e. "Root of 21 is about 4 1/2 so 3 +/- root 21 is approx 7.5 or -1.5 and so forth - all things that contribute to a secure number sense. 4. Why is the sum of the roots rational (given rational coefficients)? how about the product? The formula leads to discussions about conjugate pairs.
It seems to me that the quadratic formula offers a lot of opportunity to be playful with mathematical ideas and the notion that it can be dispensed with because calculators do it job better is only true if math is considered only as a bottom line and not as inquiry.