High/low density water solution values
Highest known is about 4.25 (all
densities in g/cm${}^3$) at room temperature:
http://en.wikipedia.org/wiki/Clerici_solution

If you're willing to allow heating it comes close to 5 because the solubility of the salts increases with temperature:
http://books.google.com/books?id=kaa2qeFRXmUC&amp;pg=PA99

My favorite runner-up is the Thoulet solution mentioned at
http://en.wikipedia.org/wiki/Potassium_tetraiodomercurate(II) but it
only reaches around 3.20.

Lowest would depend on what you mean by "water solution". If you mix a
drop of water with a gallon of a very light liquid such as diethyl
ether (which is not very miscible with water but does dissolve some
-- hence the need to dry it in the lab over sodium or molecular
sieves), then the answer is the density of the liquid (ether = 0.73).
If water has to be the majority component I'd expect the
minimum to be very close to the density of water, since mixtures tend to decrease a bit in volume. (The density of water is 1.0 at 4${}^\circ$, close to 1.0 at room temperature, 0.94 near the boiling point).