Is ArXiv popular in the statistics community? I know that the physics and math communities are very into ArXiv, but what about the stats community? Is it customary to post there before submission?
 A: All journals published by the Institute of Mathematical Statistics (IMS) -- and that includes The Annals of Statistics (one of the very top statistics journals), The Annals of Applied Statistics, etc. -- explicitly encourage authors to put preprints on arXiv and, moreover, take care of putting postprints on arXiv too. I am actually not aware of any math or physics journal that uploads papers to arXiv if the authors did not do it themselves!

The IMS encourages all members to post their articles on arXiv.
(http://www.imstat.org/publications/arxiv.html)
All IMS articles 2004 and forward are freely available in a postprint format on arXiv, as well as those articles posted by authors.
ArXiv is an open access, fully automated electronic archive and distribution server for research articles, now owned and operated by Cornell University, and partially funded by NSF. The main fields it covers are physics, mathematics, non-linear science, computer science, and quantitative biology. Recently, arXiv has cooperated with IMS and the Bernoulli Society to open up a new statistics category within mathematics. We expect this category to eventually grow into a top level archive comparable to e.g. mathematics and physics.
(http://www.imstat.org/publications/eaccess.htm)

A: Yes, Arxiv is popular in the statistics and the data science community.
As the world of stats and data science evolves everyday, it is important for statisticians and data scientists to keep themselves adept with the latest happenings, techniques and algorithms.
It might not be as popular as it is in the physics community, but it does have its share of importance in the data-rich world.
You might be interested in Gitxiv, which puts together state-of-the-art research with the corresponding open source code/libraries.
A: It is not a matter of personal opinion so let's look at some figures on terms appearing on arXiv pages (some random Google queries with few domain-specific terms):
cross validation site:arxiv.org returns

About 17,800 results

monte carlo site:arxiv.org returns

About 187,000 results

sampling site:arxiv.org returns

About 141,000 results

forecasting site:arxiv.org returns

About 11,300 results

regression site:arxiv.org returns

About 51,100 results

EDIT
As @Scortchi noticed, arXiv posts its own statistics. stat category appears in reports for the last three years as below:
year submissions % submissions
2014 2025        2.2% 
2013 1602        1.7%
2012 1284        1.5%

This however may not fully represent the content of published papers since some of them may be highly related to statistics but be tagged as different domain (e.g. as math or cs).
Also, Xi'an's blog could pose as a case study. He writes much about Bayesian statistics and often mentions arXived papers (having their own tag). 
It also seems that we mentioned "arXiv" on CrossValidated in 689 posts and comments until now (including here).
Does this make it popular or not? Still, hard to say, but for sure thousands of statistics-related papers were posted on arXiv and its popularity is growing.
