​Polyclonal antibodies are a complex mix of many different antibodies produced by multiple B-cells.  They are quick and inexpensive to produce and can be derived from a wide variety of host species, which may be important due to antigen sequence conversation between some species, or for allowing compatibility with other immuno-reagents used in your assays. As these antibodies are polyclonal they will include antibodies that recognise many different epitopes on the same antigen.  Because of their inherent heterogeneity, polyclonal antibodies are prone to batch-to-batch variability and to cross reactivity with similar antigens, however they are LESS prone to changes in the target antigen such as unfolding or denaturation.
 
Monoclonal antibodies (from hybridomas) in contrast are derived ultimately from a single B-cell that has been fused with a myeloma cell to enable it to be cultured and maintained indefinitely.*  By being derived from a single B-cell, monoclonal antibodies have a single specificity, and all of the individual antibody proteins present are identical.  For this reason they are much less likely to cross-react with related proteins, but are more likely to be sensitive to changes in the antigen protein.
 
*Hybridoma cell lines can, over time, become less productive or experience genetic instability.
 
Recombinant antibodies are monoclonal antibodies that are generated in vitro, using either synthetic or natural antibody V-genes.  This allows considerable control and manipulation of the gene sequences and the approaches used to isolate and select the antibodies.  As a result, they provide greater reproducibility and more refined/targeted binding characteristics (increased specificity) than those derived from hybridomas.