I'd never thought of it this way before, but Brendan Sexton makes an interesting point in comments:
Another important role that unions play is that they give working people a voice in politics.
Conservatives sometimes claim that workers don't [need] unions anymore because government laws now protect workers.
This seems to assume that the government and employers enacted these laws without any prompting from unions and working people mobilizing to vote. It also assumes that corporations don't try to weaken or eliminate these laws at every opportunity. And it assumes that if unions didn't exist that the GOP wouldn't get rid of those laws for their corporate clients.
Unions are also an important counterveiling force against the power of corporations in the political arena.
This is, of course, true. Absent a healthy union movement, the competition between the interest groups that actually govern our nation becomes merely a vying of different business interests, with few powerful forces advocating specifically for the interests of the working class. There is, of course, a free rider issue in the way unions work, wherein the entire working class -- of which only 8% are unionized -- can benefit from the health care expansions and worker safety regulations and guaranteed maternity leave benefits and all the other worker-friendly legislation the labor movement convinces the Democrats to pass, even as the average American doesn't realize it's unions doing the bulk of the organizing behind these measures.