The tendency for expenditure Engel curves to flatten out at high income levels is frequently cited as evidence that major shifts in household spending patterns take place as households become more affluent. Empirically, little has been done to examine (i) how pervasive this tendency is across the Engel curves of different goods and services, (ii) whether the rate at which Engel curves flatten out may significantly change over time and (iii) how robust Engel curves are in the face of changes in the income distribution of households. Using data from the UK Family Expenditure Survey, we find evidence that the tendency for Engel curves to flatten out, which we dub 'saturation', is indeed widespread across a wide range of goods and services. However, a tendency for their shape to shift over time, and for these shifts to co-move with changes in the income distribution of households, casts some doubt on whether the declining slope of Engel curves can be used to predict slowdowns in the growth rate of demand for particular goods and services.