We have developed a procedure for synthesizing large stable branched DNA structures that enables visualization via fluorescence microscopy. Using this procedure we have synthesized large DNA stars and observed their electrophoretic behavior in polymer solutions and gels. In dilute polyacrylamide solutions, the DNA stars move as random coils and appear to experience only brief collisions with the polymer chains in solution. The effect of polymer solution concentration on the electrophoretic mobility of stars in the dilute regime is found to be in good accord with predictions of the transient entanglement coupling (TEC) model. In semidilute polymer solutions, the star arms extend in the field direction and drag the core through the matrix. The star arms form several U-shaped conformations as they collide and engage with polyacrylamide chains. The U-shaped conformations occasionally evolve into J-shaped conformations as the star arms slide off the matrix chains they engage during electrophoretic migration. In concentrated polymer solutions, the arms of the star extend and form V-shaped structures with the core as the apex. The arms then pull the core through the matrix. These V-shaped conformations are much longer-lived than U-shaped ones and, unlike the latter, do not transform to J-shaped conformations. In polyacrylamide and agarose gels, where matrix entanglements are fixed, DNA stars become trapped when entanglements with matrix molecules prevent the core from being pulled through the matrix by the extended arms. This trapping was observed at all gel concentrations and electric fields studied.