What is the average teaching load for tenure faculty in mathematics? I am interested in Math, specifically pure Math, in the USA. I will be on the job market soon for a tenure track position and mathjobs ads usually do not specify the teaching load. 

What is the average teaching load of tenured faculty (in pure math say) at a research university? (and let's say we are talking about faculty members who are still very much research active)

I've met faculty who teaches 1+1 (or even 0+0...), 2+1 or even 2+2. But I don't have a good general picture of how much teaching is done (partly because I haven't studied in the US).
In mathematics departments at U.S. research universities, typical teaching loads are 1+2 or 2+2, with 1+2 being common at fancier or better funded schools.  See this chart for some data; I don't know how accurate it is, but it looks approximately right to me.  1+1 is not absolutely unheard of, but it is very rare.  Of course what counts as a "research university" is unclear, and some places that consider themselves research universities may have 2+3 loads, but I don't think any of the more prestigious research universities have 2+3.

Of course there are a lot of other factors that come into teaching load.  How much flexibility is there in the course assignments?  How does the teaching credit differ between huge lecture courses and small graduate seminars?  How many people (if any) get a reduced teaching load?  Does the department allow faculty to buy out of teaching using grant funds?  Without answers to questions like these, a numerical comparison of teaching loads only tells you so much.  What I'd recommend is that you apply for every job you might plausibly want, and then once you start to get interviews or offers you can look into the teaching conditions at these schools in detail.