In the last several national elections, 527 groups have had the biggest impact on third-party (not connected to the candidate's campaign) spending. The "Swift Boat" 527 was a major influence on the national conversation during the 2004 Presidential election between President Bush and John Kerry.
Interestingly, there seems to be a reason why Democrats are so up in arms about the Supreme Court ruling. The website Open Secrets has a page devoted to political expenditures by 527s during the last few election cycles. They've even got the information broken down into handy categories. For example, here is the information on "Democrat/Liberal" 527s:
Now, here's the information for "Republican/Conservative" 527s: