Several applications require strong noncovalent adhesion of polymers to substrates. Graft and branched polymers have proven superior to linear polymers, but the molecular mechanism is still unclear. Here, this question is addressed on the single molecule level with an atomic force microscopy (AFM) based method. It is determined how the presence of side chains and their molecular architecture influence the adhesion and the mobility of polymers on solid substrates. Surprisingly, the adhesion of mobile polymers cannot significantly be improved by side chains or their architecture. Only for immobile polymers a significantly higher maximum rupture force for graft, bottle-brush, and branched polymers compared to linear chains is measured. Our results suggest that a combination of polymer architecture and strong molecular bonds is necessary to increase the polymer-surface contact area. An increased contact area together with intrachain cohesion (e.g., by entanglements) leads to improved polymer adhesion. These findings may prove useful for the design of stable polymer coatings.