What adjective do you use to describe a curve that's very curved?"

Solution 1:

A hairpin curve, hairpin turn or hairpin corner:

• a very sharp curve in a road, where the road forms a "U" shape

• A hairpin turn (also hairpin bend, hairpin corner, etc.), named for its resemblance to a hairpin/bobby pin, is a bend in a road with a very acute inner angle, making it necessary for an oncoming vehicle to turn almost 180° to continue on the road. Such turns in ramps and trails may be called switchbacks in American English, by analogy with switchback railways.

http://en.wikipedia.org/wiki/Hairpin_turn

http://www.macmillandictionary.com/us/dictionary/american/hairpin-curve

An acute-angled curve:

http://en.wikipedia.org/wiki/Angle#Types_of_angles

Solution 2:

'Extreme', 'severe', or 'sharp' all seem good to me.