A common problem with implants is that bacteria can form biofilms on their surfaces, which can lead to infection and, eventually, to implant rejection. An interesting strategy to inhibit bacterial colonization is the immobilization of silver (Ag) species on the surface of the devices. The aim of this paper is to investigate the action of citrate-capped silver nanoparticles (AgNPs) on clinically relevant Gram-positive (Staphylococcus aureus) and Gram-negative (Pseudomonas aeruginosa) bacteria in two different situations: (i) dispersed AgNPs (to assess the effect of AgNPs against planktonic bacteria) and (ii) adsorbed AgNPs on titanium (Ti) substrates, a material widely used for implants (to test their effect against sessile bacteria). In both cases, the number of surviving cells was quantified. The small amount of Ag on the surface of Ti has an antimicrobial effect similar to that of pure Ag surfaces. We have also investigated the capability of AgNPs to kill planktonic bacteria and their cytotoxic effect on UMR-106 osteoblastic cells. The minimum bactericidal concentration found for both strains is much lower than the AgNP concentration that leads to cytotoxicity to osteoblasts. Planktonic P. aeruginosa show a higher susceptibility to Ag than S. aureus, which can be caused by the different wall structures, while for sessile bacteria, similar results are obtained for both strains. This can be explained by the presence of extracellular polymeric substances in the early stages of P. aeruginosa biofilm formation. Our findings can be important to improving the performance of Ti-based implants because a good bactericidal action is obtained with very small quantities of Ag, which are not detrimental to the cells involved in the osseointegration process.