In the U.S., just 7.5% of private-sector workers are union members, and about 12% of all workers, including government workers. In the euro zone, 18% of private-sector workers and 22% of all workers, are unionized.
Unions themselves are neither good nor bad for the economy. In fact, theoretically, unions provide stability to workers and reduce replacement and retraining costs for employers, so they should be economically favorable. The problem with modern-day unions, especially government unions, is their benefits, such as pension and health care liabilities, are uncertain. Without some direct tie-in to the present value of funds in the budget, government union benefits could expand exponentially, sapping more and more taxpayer dollars. In addition, many union negotiations occur behind closed doors, providing no check on expanded taxpayer liabilities.
No business or government can survive by continuing to add undefined, potentially unlimited benefits while running major deficits.
More on California's government unions HERE. More on California's teachers' unions HERE.
More on the general topic of government unions here (Warren Buffett); here ("Rotting from Within"); and here (Road to Bankruptcy).
Update on February 15, 2010: the NYT and Phyllis Korkki have their own percentages on union membership HERE. Basically, in 2009, 12.3% of wage and salary workers were union members. 7.9% of the aforementioned 12.3% were government workers, meaning just 4.4% of private sector workers were unionized.
Among government workers, local government workers like teachers, cops, and firefighters (as opposed to state and federal government workers) had the highest rate of public sector membership, at 43.3%.
See THIS chart for more information (Catherine Rampell, NYT, June 1, 2010). In California, 13.7% of all employees were state and local government employees in 2009. That doesn't sound like a huge percentage, but most elections inspire only 50% to 70% of eligible voters to come out and vote. That means union members often supply 20% to 25% of the total voters on a proposition or candidate.
Update on May 3, 2012: according to a Alasdair Roberts Bloomberg article ("Can Occupy Wall Street Replace the Labor Movement?") published May 1, 2012,
"In 1981, the labor movement was already in decline, and the trend accelerated afterward. In 1960, one-third of the private-sector workforce had been represented by trade unions. Today, only 8 percent is. The missing army of private-sector union members--that is, the number of additional workers that the movement would include today if unionization rates had stayed at levels of the 1960s and 1970s--is about 20 million people."
Update on May 7, 2012: Amanda Paulson, Christian Science Monitor (online, seen May 7, 2012):
"Less than 7 percent of private-sector workers now belong to a union, compared with more than 30 percent in the 1950s. Since 1983, about 3 million fewer people are represented by unions...The public sector, however, has been somewhat cushioned...Some 36 percent of state and local workers belong to unions (and that includes "right-to-work" states that prohibit union-only workplaces and have far smaller union rosters)."
Update on December 12, 2012: CNN has a map that shows union membership per state: http://money.cnn.com/interactive/news/economy/union-membership-by-state/