Is elasticity of substitution between goods empirically constant? In New Keynesian models, we use a lot of CES assumption, usually Dixit-Stiglitz, to develop an economic model. Is CES, constant elasticity of substitution between goods, empirically (approximately) true?
Constant elasticity of substitution (CES) Utility functions imply demand functions that are linear in (i.e. conditional on prices they are constant fractions of) income (see Rutherford's Lecture Notes on Constant Elasticity Functions). However, there is empirical evidence for both superior goods (demand that increases faster than income) and inferior goods (goods that decrease in income), this does not actually hold for real preferences. 

The fact that household budget shares on each consumption good (or even category) are not constant is probably additional evidence against CES. In principle it is explainable if different consumers face different costs for goods but shouldn't explain why some people choose to do entirely without certain categories of consumption (no TV rather than an inexpensive one). I say probably because: 


If you define the category wide enough (say two, durable and non-durable consumption), everyone does likely does consume something in every category and maybe in close to fixed proportions. 
For certain important forms of consumption like cars and house, adjustment costs and indivisibility may make households face very different prices.


But, as @regressforward suggests, it may still be an acceptable approximation.