If I'm going to throw numbers around I should have a credible source I can immediately cite. I didn't just make up that number but I didn't research it as thoroughly as I should have. So here is the research behind it now:
Originally I found the 10,000 per day number from a Christian anarcho-capitalist website (yes, they exist, imagine my surprise!). Originally I didn't look into the source they cite, but in independent searching I ended up discovering the same source they used. Professor R.J. Rummel (http://en.wikipedia.org/wiki/R._J._Rummel) has spent 15 years assembly data on what he calls "democide"--murder by the State. He came up with 262,000,000--262 million deaths caused by governments, with this number excluding combat deaths (which I think should be included as essentially all large scale wars are conducted by States). Here's a link to his website:
262,000,000/100 = 2,620,000 per year
2,620,000/365 = 7,178 per day. So my 10,000 number was off by a significant amount because I think my original source included combat deaths and executions .
So now I'll restate my statistic: Governments killed over 7,000 people every day during the 20th century. This does not include combat deaths or executions. There were about 19 million (low estimate) combat deaths in World War II ALONE, which adds about 500 per day. Then if you include WWI, the American Civil War, etc. etc. it could easily get up toward 10,000. But regardless, 262 million people or 7000 a day is a horrendous number.
World War II statistics:
(Note that Rummel is referenced in the second website.)
Thank you Richard for the peer review and keeping me accountable.