Is there an index that describes how differentiated a product is? Some products are commodities, identical regardless of the producer. Others are very different an people look for specific brands of whatever they buy. Has anybody built any sort of index of how differentiated a product is or an industry? This would be very useful for research purposes!
For an industry, one indicator used by competition authorities is the Herfindahl–Hirschman Index measured as $\displaystyle \sum_{i=1}^N s_i^2$ where there are $N$ firms in the sector and the market share of the $i$th firm is $s_i$. 

This gives a value of $1$ when there is a single firm and $\frac1N$ when the $N$ firms have equal market shares, but also deals sensibly with cases where different firms have different shares.

For a particular product, you could look at something else like comparing its price elasticity of demand when other similar products do not change price, perhaps comparing this with the price elasticity of demand for all the similar products together.  An undifferentiated product should have an almost infinite price elasticity as all demand will shift if there is any relative price change.