Antimicrobial resistance (AR) mechanisms encoded on plasmids can affect other phenotypic traits in bacteria, including biofilm formation. These effects may be important contributors to the spread of AR and the evolutionary success of plasmids, but it is not yet clear how common such effects are for clinical plasmids/bacteria, and how they vary among different plasmids and host strains. Here, we used a combinatorial approach to test the effects of clinical AR plasmids on biofilm formation and population growth in clinical and laboratory Escherichia coli strains. In most of the 25 plasmid-bacterium combinations tested, we observed no significant change in biofilm formation upon plasmid introduction, contrary to the notion that plasmids frequently alter biofilm formation. In a few cases we detected altered biofilm formation, and these effects were specific to particular plasmid-bacterium combinations. By contrast, we found a relatively strong effect of a chromosomal streptomycin-resistance mutation (in rpsL) on biofilm formation. Further supporting weak and host-strain-dependent effects of clinical plasmids on bacterial phenotypes in the combinations we tested, we found growth costs associated with plasmid carriage (measured in the absence of antibiotics) were moderate and varied among bacterial strains. These findings suggest some key clinical resistance plasmids cause only mild phenotypic disruption to their host bacteria, which may contribute to the persistence of plasmids in the absence of antibiotics.