Organic aerosol particles are known to often absorb/desorb water continuously with change in gas phase relative humidity (RH) without crystallisation. Indeed, the prevalence of metastable ultraviscous liquid or amorphous phases in aerosol is well-established with solutes often far exceeding bulk phase solubility limits. Particles are expected to become increasingly viscous with drying, a consequence of the plasticising effect of water. We report here measurements of the variation in aerosol particle viscosity with RH (equal to condensed phase water activity) for a range of organic solutes including alcohols (diols to hexols), saccharides (mono-, di- and tri-) and carboxylic acids (di-, tri- and mixtures). Particle viscosities are measured over a wide range (10^-3 to 10^10 Pa s) using aerosol optical tweezers, inferring the viscosity from the timescale for a composite particle to relax to a perfect sphere following the coalescence of two particles. Aerosol measurements compare well with bulk phase studies (well-within an order of magnitude deviation at worst) over ranges of water activity accessible to both. Predictions of pure component viscosity from group contribution approaches combined with either non-ideal or ideal mixing reproduce the RH-dependent trends particularly well for the alcohol, di- and tri-carboxylic acid systems extending up to viscosities of 10^4 Pa s. By contrast, predictions over-estimate the viscosity by many orders of magnitude for the mono-, di-, and tri-saccharide systems, components for which the pure component sub-cooled melt viscosities are >>10^12 Pa s. When combined with a typical scheme for simulating the oxidation of a-pinene, a typical atmospheric pathway to secondary organic aerosol (SOA), these predictive tools suggest that the pure component viscosities are less than 10^6 Pa s for ~97% of the 50,000 chemical products included in the scheme. These component viscosities are consistent with the conclusion that the viscosity of a-pinene SOA is most likely in the range 10^5 to 10^8 Pa s. Potential improvements to the group contribution predictive tools for pure component viscosities are considered.