We investigate how the large-scale surface magnetic fields of cool dwarf stars, reconstructed using the Zeeman-Doppler Imaging (ZDI) technique, vary with age, rotation period, Rossby number and X-ray emission. Our sample consists of 104 magnetic maps of 76 stars, from accreting pre-main sequence to main-sequence objects, spanning ages from ~1 Myr to ~10 Gyr. For non-accreting dwarfs we empirically find that the unsigned average large-scale surface magnetic field relates to age as age-0.65. This relation has a similar power dependency to that identified in the seminal work of Skumanich (1972). We also find in our data evidence for a linear-type dynamo, in which the surface field is linearly dependent on the rotation rate. The trends we find ...