Off-the-cuff thoughts (more considered ones may come later):
His record of legislative accomplishment, which was very impressive even if one did not agree with every one of his positions, was a tribute both to his own skill and that of his staff, which was always one of the best in the Senate. (Not that I knew this first-hand, but it was what everyone said.)
In 1980 I supported his campaign for the Democratic nomination and even ran as a candidate for Kennedy delegate. (I think I might have gotten ten votes or so; I know my late grandmother voted for me because I personally escorted her to the voting booth.) One of the most vivid political memories I have is watching Kennedy's speech at the 1980 Democratic convention, probably the greatest convention speech of the last 40 or 50 years. It was written by Robert Shrum and delivered superbly by Kennedy. The line in the speech about Ronald Reagan having no right to quote FDR still sends shivers down my spine. Great stuff. Kennedy will be missed, especially now with health care reform on the front burner. R.I.P.
P.s. John Sides links to an audio clip from the 1980 speech.
And National Journal collects reminiscences of former aides and others.