Cosmological simulations of galaxy formation often rely on prescriptions for star formation and feedback that depend on halo properties such as halo mass, central overdensity, and virial temperature. In this paper, we address the convergence of individual halo properties, based on their number of particles N, focusing, in particular, on the mass of halos near the resolution limit of a simulation. While it has been established that the halo mass function is sampled on average down to N ~ 20-30 particles, we show that individual halo properties exhibit significant scatter, and some systematic biases, as one approaches the resolution limit. We carry out a series of cosmological simulations using the Gadget2 and Enzo codes with Np = 643 to Np = 10243 total particles, keeping the same large-scale structure in the simulation box. We consider boxes of small (l box = 8 Mpc h –1), medium (l box = 64 Mpc h –1), and large (l box = 512 Mpc h –1) size to probe different halo masses and formation redshifts. We cross-identify dark matter halos in boxes at different resolutions and measure the scatter in their properties. The uncertainty in the mass of single halos depends on the number of particles (scaling approximately as N –1/3), but the rarer the density peak, the more robust its identification. The virial radius of halos is very stable and can be measured without bias for halos with N 30. In contrast, the average density within a sphere containing 25% of the total halo mass is severely underestimated (by more than a factor 2) and the halo spin is moderately overestimated for N 100. If sub-grid physics is implemented upon a cosmological simulation, we recommend that rare halos (~3σ peaks) be resolved with N 100 particles and common halos (~1σ peaks) with N 400 particles to avoid excessive numerical noise and possible systematic biases in the results.