When did/will peak conventional oil happen?
The answer depends a lot on what you mean by "excluding shale oil".  Tight oil production, commonly referred to as "shale oil" is about 4 million barrels per day currently (2014), compare to almost none in 2005.  

Canadian oil sands production is at 2 millon barrels per day, compare to about 700,000 per day in 2005.

So compare to 2005, tight oil (shale oil) and oil sands production is up about 5 million barrels per day.   

Now look at total world oil production:



From the graph it can been seen that subtracting out the 5 million barrels/day of unconventional production, world production is somewhat below the 2005 level. (Quantitative values were 73.9 M bbl/day in 2005; 76.9 M bbl/day in first 8 months of 2014)

With the expectation that tight oil and oil sands production will increase in share of the production, it is entirely possible that the peak in conventional production has already occurred.