It is always recommended to replace suspecsion and braking components on both sides of the same axle at the same time, wherever possible.
Both will currently be the same age - if one has failed, it is likely that the other is in a similar condition and so could easily fail soon. In the case of springs, the constant flexing of the metal can eventually lead to fatigue, which is presumably the cause of the first failure - the other spring will be similarly fatigued. Similar arguments apply to other components such as shocks and bushes, which all wear out over time.
Additionally I suspect (although I'm not a metallurgist, so this is just speculation) that the spring rate will change over time and use, so a new spring would be slightly harder than the old one - if that is the case then it would result in uneven handling, which would be very dangerous. This is certainly the case with shock absorbers, which lose their damping ability as they wear - one side well damped and the other not would be deadly!