Why buy a more expensive kitchen scale
Although I've come to find a lot of uses for my kitchen scale, the ones that immediately pop into mind are:


Exact measurements.  When a recipe
calls for a cup of baby spinach, for
example, that's going to be hard to
measure.  Not going to be a problem
if you're dealing with weights.  This is extremely important with baking, where exact measurements are absolutely necessary.  Ideally, the recipe would have both,
but if not you can often convert via
the nutritional info on the bag -
it'll say something like 1 cup (28g).  A cup of flour varies wildly depending on various factors, for example whether or not it was sifted.
Portion control.  I helped my wife do
Weight Watchers before our wedding,
and I can't imagine trying to figure
out 1 portion (3oz) of lean meat without it.
Learning.  I'll weigh a piece of meat
before and after cooking it to see
what kind of weight loss I get from
moisture, for example.


When buying, you want to think about the following:


Capacity.  Cheap models often only go to 5lbs, whereas more expensive can hit 10 or 15.  Becomes important when you're cooking in bulk, may not be important depending on your cooking habits.
Digital vs balance. I don't trust balance (analog) scales, they're too easy to have become uncalibrated, and I don't want to be calibrating every time I need to use it.  Digital scales are easier to read, and very easy to go between US standard and metric measures.  Also, digital scales have a tare feature, which is invaluable (as KeithB pointed out).
US standard/metric.  You definitely want a scale that can do both, recipes may have either.  Most scales should handle this.
Plate/bowl. I find that scales that come with a bowl are unnecessary, I prefer one with a nice large plate that I can put my own bowl onto.  With the tare feature that almost all digital models have, you can zero out your weight so you can pick any bowl to meet your needs.  The larger the plate, the better, so you can fit more stuff on it if you're not using a bowl.


As far as price goes, I think $20 is too cheap, and is likely to become unreliable quickly, if not immediately.  That said, I think over $100 is too much as well, that's likely to be based on design or name.  My current scale cost me about $50 and works great, and I check its calibration regularly and haven't had a problem yet.

One specific example from our house - I make smoothies every morning from 20 oz frozen fruit, 10 oz soy milk, 6 oz greek yogurt.  My wife is following a very specific nutrition guide right now, so I then split it into 12oz for her, 24oz for me.  Getting her nutritional info right without a scale would be all guesswork (and I've come to learn, through using my scale, that my guesswork used to be pretty far off - it's much better since I started using the scale regularly).