Protein expression is a stochastic process that leads to phenotypic variation among cells. The cell-cell distribution of protein levels in microorganisms has been well characterized but little is known about such variability in human cells. Here, we studied the variability of protein levels in human cells, as well as the temporal dynamics of this variability, and addressed whether cells with higher than average protein levels eventually have lower than average levels, and if so, over what timescale does this mixing occur. We measured fluctuations over time in the levels of 20 endogenous proteins in living human cells, tagged by the gene for yellow fluorescent protein at their chromosomal loci. We found variability with a standard deviation that ranged, for different proteins, from about 15% to 30% of the mean. Mixing between high and low levels occurred for all proteins, but the mixing time was longer than two cell generations (more than 40 h) for many proteins. We also tagged pairs of proteins with two colours, and found that the levels of proteins in the same biological pathway were far more correlated than those of proteins in different pathways. The persistent memory for protein levels that we found might underlie individuality in cell behaviour and could set a timescale needed for signals to affect fully every member of a cell population.