I would like to test the influence of solvation parameters in implicit solvation models and wonder which codes are freely available as standalone programs for protein folding of small proteins, and which use energy minimization approaches instead of dynamics, so I am not looking for molecular dynamics codes.
The most popular molecular dynamics codes are namd and gromacs, and maybe also desmond. These packages are freely available and "open source" in the sense that the source code is made available for free. Wikipedia hosts a list of software for molecular modeling which may contain other good links.
These codes, however, are also quite complex and therefore if you want to make changes of your own, e.g. to test new solvation models, you might spend quite a bit of time just trying to understand them. If ease of use trumps speed (probably not completely if you're looking at time-scales for folding), you might want to look at mmtk, which lets your program custom molecular dynamics simulations in Python.
If you're interested in speed, but not all the bells and whistles of a full-fledged simulation package, you may also be interested in molecular dynamics libraries such as OpenMM or mdcore (disclaimer: mdcore is my own software project). These will, however, require quite a bit more programming on your own side.
The term "energy minimization" usually refers to the minimization of the potential energy. For protein folding simulations, you really need to minimize free energy. If you run plain energy minimization on an unfolded protein, you will pretty soon get stuck in a local minimum. So you probably do want molecular dynamics, and use some protocol such as simulated annealing in order to get to progressively lower energies. See the answer by pedro for software suggestions.
There is also an interesting program called foldit which looks like a puzzle game with a nice GUI but in the background it actually studies protein folding.