This thesis reports measurements at the single atom scale by using low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS). Different sample systems where analyzed with normal conducting and superconducting tips. Chapter 2 presents the theoretical aspects which have to be taken into account for a detailed analysis and a consistent interpretation of the STS measurements. In chapter 3 the creation of a hexagonally ordered superlattice of single Ce adatoms on Ag(111) is reported and understood within a scattering model of the surface state electrons with the adatoms. Furthermore, the change in the local density of states of the surface state in ordered and slightly disordered superlattices is measured and theoretically explained within a tight-binding model which allows to understand the creation and stability of the superlattice by an energy gain of the participating surface-state electrons. Because Ce atoms have a non-vanishing magnetic moment which is expected to interact with the continuous states of the supporting surface leading to a Kondo resonance, chapter 4 presents measurements on single Ce adatoms on different Ag surfaces. This chapter shows the difficulties to interpret the obtained data. For instance, bistable Ce adatoms are detected on Ag(100) which show drastical changes in their apparent height and spectral signature depending on the tunneling conditions. The possible physical processes behind these phenomena are discussed. While the results presented in the first chapters were obtained with a normal conducting tip, chapter 5 intensively discusses the opportunities superconducting tips offer in low-temperature STS measurements. Novel insight in and thorough understanding of Andreev reflection processes are obtained by using the unique possibility of having different superconducting gaps in the tip and the sample. Detailed analyses of the supercurrent at low tunneling resistances reveal tunneling currents which are not described within the standard resistivity shunted junction model, and are presumably due to self-induced tunneling or due to an additional quasiparticle tunneling channel which only exist in asymmetric junctions. Furthermore, the influence of single magnetic Co atoms inbetween the superconducting tunnel junction on the obtained spectrum is discussed.