Machine Learning is a fast moving field, and many papers are incremental improvements, so an always up-to-date list will be unlikely. None the less, there are quite a few lists out there if you look. Here are some I've seen posted recently:

https://news.ycombinator.com/item?id=8728112

http://deeplearning.stanford.edu/wiki/index.php/UFLDL_Recomm...

http://www.cs.toronto.edu/~hinton/deeprefs.html

http://arxiv.org/abs/1404.7828

Probably the most famous papers is Breimen's "The Two Cultures". The rejoinder's from Cox and Hoadley add two additional perspectives from long careers.

The OP already did this for ML too. Read the title again, "every programmer", don't you think people doing ML are programmers? :-D