What advantages does a neuron with multiple dendrites have? What advantages does a neuron with multiple dendrites have, as opposed to one with fewer dendrites?
More dendritic input makes a neuron more suitable as an integrator. The more dendrites a neuron has, however, the less faithful it will transmit a single incoming signal, as other incoming input may interfere with transmission. Hence, a neuron with a single dendrite will be better suited to faithfully relay incoming signals.  

Among the most faithful neurons are the cone bipolar cells in  the central part of the retina, who receive a single input and transmit a single output (Purves et al., 2001) via a single axon to the retinal ganglion cell who's axons make up the optic nerve, while on the other end of the spectrum there are, e.g., the Purkinje cells in the cerebellum that can receive input from as many as 80,000 fibers (Konnerth et. al, 1998).

References
- Konnerth et. al, PNAS (1998); 87: 2662-5
- Purves et al. (eds.), editors. Neuroscience. 2nd ed. Sunderland (MA): Sinauer Associates (2001) Functional Specialization of the Rod and Cone Systems