There have been a variety of prizes to solve problems that are practical such as space rocket. Some companies have made a business out of problem solving through mediating solvers and problem generators – such as those mediated by Innocentive. However, rarely are problems solved just for the sake of solution of the problem. One such exception is Clay Mathematics institute, founded by Landon T Clay and Lavina D Clay. Their mission is to solve problems and encourage development of mathematics.
Their problems are mostly theoretical such as the ones in the link below. What is unusual is that they have a list of 7 unsolved problems and each of them has a $1 Million prize to solve the problem. The conditions to achieve solution are complex but very rarely has any prize been assigned for solving a theoretical problem.
The only problem that is close to being practical in their list is the Navier-Stokes equation which governs turbulence measurements. A solution to this problem requires understanding of the equation. If solved the impact would touch almost all motion of planes, trains and cars, insects, birds as well as fluid flow.
Solvers welcome.