Alpine ski design has changed dramatically in recent years. In general, they're shorter and more parabolically shaped than they were just a few years ago. The new ski designs have ushered in a new school of ski instruction. We teach concepts of edging your skis and turning your feet to steer where you want to go, as opposed to the old school dump and shove. These modern techniques are made very difficult for beginners on skis that are too long, so if you put you kids on your old long skis and stick them in a beginner lesson they will probably have a very bad experience. Standards of optimal ski lenth have continued to change year after year but they now ('05-'06 season) seem to be leveling out. IF YOU STAND A MODERN SKI UP IN FRONT OF YOU IT SHOULD RISE TO BETWEEN YOUR CHIN AND YOUR MOUTH. There are instances where a longer ski may be appropriate (competitive racing for example) but if you're looking for answers here, just reread that sentence in caps.
-Certified Level II instructor, Professional Ski Instructors of America

From the rec.skiing newsgroup FAQ:

There are standard formulas relating your skill level, weight and height to a nominal ski length. For alpine beginners length's center around 160 CM, intermediates around 180 CM and experts around 195 CM. Weight modifies these by about 10 CM in either direction and some people argue about whether height matters at all. Note that it is not a good idea to use skis longer than you are comfortable with (don't let ego decide), but once you reach a certain level of proficiency most people can work up to an "expert" lengths with little difficulty. This is a good reason for renting, rather than buying skis during the learning stages.

For classical nordic skiing some people reccommend a XC ski length that comes up to your upraised wrist, but this can end up specifying a ski that's way too long, especially if you're long-limbed or light for your height. In any event, the ski should be no longer than this, and no shorter than about 6" taller than your height. A ski that's too long will be difficult to control and may be too stiff. For skating the skiis will be somewhat shorter, although skating on classical skiis is possible (slightly better technique required...) In general get fitted by a professional, not by someone who sells toasters and TV's.