I've seen a lot of good items about George McGovern (here's the NYT obituary) so I'll focus on what I know the most about: presidential nomination reform.
Granted, I may be biased here (we all tend to inflate the stuff we study), but I'll just say that there are very few people who have their name attached to such an important change in the way the nation governs itself.
Do you all know the story? In 1968, young anti-war activists went "Clean for Gene" -- at least as legend has it, they shaved, got haircuts, put on regular people clothes, and went up to New Hampshire to campaign for Gene McCarthy. And at first it looked as though it was working. McCarthy did surprisingly well in the New Hampshire primary; next thing you know Bobby Kennedy entered the contest as another antiwar candidate, and then, shocking everyone, LBJ abdicated, saying he wouldn't run again. What followed were a small series of primaries, the assassination of Kennedy, and then the growing revelation (to those new to the process) that none of those primaries really counted for anything. Hubert Humphrey was nominated in Chicago, by delegates who had been chosen far in advance of the campaign, in many cases under procedures which appeared to be (and often were) entirely closed to those new to party politics.
The reformers didn't get the nomination, but they did get a reform commission, chaired by George McGovern. What happened next (and the way it happened is told in Byron Shafer's terrific Quiet Revolution) is they completely changed the method of nominating candidates for president. The convention system had endured for over a century since it replaced King Caucus; suddenly, it was cast aside for the new, primary/caucus delegate accumulation system.
Brief version: in the old system, candidates competed to win the support of delegates, who were the representatives of the state parties. In the new system, candidates competed to have their own delegates selected in primaries and multistage caucuses which were equally open and accessible to (at least) all party members.
At first, this seemed to mean a transfer of influence away from the parties and towards the candidates, on the one hand, and the press, on the other. The result were two Democratic nominations, McGovern himself in 1972 and Jimmy Carter in 1976, that almost certainly would not have happened under the pre-reform rules. However, it turned out that those nominations were probably effects not of the rules per se but of uneven adaptation to the rules by various party actors. By 1984, and in later years, it became clear the new procedures allowed parties understood properly -- which included party networks outside of the formal party structure -- to choose the nominee.
None of this is to say that the current procedures are perfect. For example: one of the key complaints from 1968 was that it was unfair that so much of the nomination process was locked into place well before the election year; activists were outraged to find that the delegates had been chosen long before McCarthy's campaign had got underway. This was enshrined in McGovern-Fraser commission guidelines for "timeliness" which required that delegates would be selected in the election year. And yet those pre-chosen delegates could be influenced right up until the convention, at least in theory; now, while the delegates are chosen in January through June, much of the real action of the campaign happens long before the voters get involved. And some have argued that the convention system was doomed one way or another.
The new system promised full, meaningful, and timely participation. I'm not sure whether it really achieved those goals. However, I do think that the commission successfully achieved the most important goal, which was to make the party more permeable to new party actors and new issues. Given all that was happening to parties and politics in general at the time, and then in the subsequent decades, I think that's a pretty good accomplishment.