this one or this one ).
Regardless of how the senator was killed, his pro-worker, pro-women and pro-liberal legislation left an impact on American Politics. Wellstone's legacy (well documented in this piece in the Atlantic) continues on today in the work of the Wellstone Foundation.
But had Wellstone not died in the crash, it would have dramatically changed the history of the past decade and the actions of the Bush Administration (and future administrations after that - as I will detail below, I doubt an Obama presidency would have occurred at this point).
Wellstone was the only senator to vote against the War in Iraq. He also voted against the Department of Homeland Security. Wellstone was an enemy of the Bush-Cheney team. Just days before he died, Wellstone met with Cheney to vote his displeasure of the course in Iraq. Had Wellstone been elected, the first major change would have been democrat control of the US Senate. Wellstone said that his vote against the war in Iraq would likely cost him the election, but in polls leading up to the election, Wellstone was leading. Votes that come "out of the wood work" in Minnesota caused the defeat of Wellstone's predecessor, Norm Coleman, losing to democrat comedy writer Al Franken (yes, Wellstone would have probably kept SNL out of the US Senate).
Wellstone's opposition would have made him an extremely popular democrat in the 2004 election cycle. The vice president selected by John Kerry, John Edwards, was a recently elected senator. While the Edwards choice was an attempt to revitalize southern democrats in the way that Bill Clinton did, a Wellstone VP pick would have helped tremendously in the midwest. However, Wellstone had no known intentions to seek higher office. Regardless, the 2004 DNC, which was highlighted by Barack Obama's keynote address, would have had another major contributor in Wellstone's anti-war voice. The 2004 election was close - it's impossible to say for certain, but Wellstone campaigning with John Kerry and John Edwards in Florida and Ohio certainly would have helped the effort. While Ohio was putting anti-gay legislation on the ballot to fire up conservatives who would vote for Bush, the democrats could have rallied their troops strongly behind Wellstone (who wasn't in an election cycle of his own) and his anti-Iraq message - popular especially with younger voters.
In my opinion, had the democrats played the Wellstone asset the right way in 2004, they would have won the election - but the democrats did so many things wrong in 2004 - they somehow allowed a criticism that their candidate came home and protested the Vietnam War in an unpatriotic way, while the republican's candidate was a draft dodger! In hindsight, that's hilarious, isn't it? Let's say that the John Kerry/John Edwards team won the election in 2004 - the scandals of Edwards personal life and death of his wife before and during his electoral term would not have allowed Edwards to remain as vice president. Obviously Wellstone (and Hilary Clinton) would have been high up the list to succeed Edwards. Also, Kerry would have been less likely to allow some of the deregulation that occurred which led to the banking crisis of 2007 and Kerry would have had to have ended the war in Iraq quicker. I'm sure there'd have been some recession, because these things are cyclical, but I don't think it would have been to the same extent. If Kerry had an Iraq timetable on the table as part of a 2008 re-election campaign, he wouldn't have lost. John McCain would not have run against John Kerry, so your 2008 GOP ticket could have been Mike Huckabee and (hopefully?) a more centrist republican like Tom Ridge. I think Kerry would have a tougher time get elected than re-elected.
As for this election, as stated before, there's no reason to think Paul Wellstone would have been seeking higher office and there were so many in the vast far-right bureaucracy that would have made him the target for the republican party in the way Hilary Clinton was during the 2000s. But Wellstone or not, Kerry would have been handing off a fairly strong US to the vice president he choose to succeed John Edwards (which would have likely been the biggest scandal of a Kerry presidency). Barack Obama, now finished with one full term as senator may be running for the presidency had Kerry somehow not been re-elected. The Tea Party movement probably exists in a much smaller form.
This is all speculation - but it goes without saying that I believe the country would have been better if Wellstone's plane landed uneventfully on that runway 10 years ago today.