We compute the partition function of the Potts model with arbitrary values of q and temperature on some strip lattices. We consider strips of width L-y = 2, for three different lattices: square, diced and 'shortest-path' (to be defined in the text). We also get the exact solution for strips of the Kagome lattice for widths L-y = 2, 3, 4, 5. As further examples we consider two lattices with different type of regular symmetry: a strip with alternating layers of width L-y = 3 and L-y = m + 2, and a strip with variable width. Finally we make some remarks on the Fisher zeros for the Kagome lattice and their large q-limit.