I find it amazing that the people of Massachussetts repeatedly
re-elect Sen. Kennedy despite what happened to poor Mary Joe Kopechne.
 Whether the truth about what happened to her is clouded by accident
or design, at the very least he has the same culpability that anyone
driving a car would if a passenger dies in an accident of their
making.  Or at least, that's what I would assume.
 In an age where small indiscretions can derail a political career,
why has the death of a young woman not been an obstacle to re-election
for Ted Kennedy?

Whole bunch of reasons. The Kennedys' are a dynasty in Massachusetts,
and that helps forgive a lot of mistakes. Also, Massachusetts is
liberal, so there isn't an inherent conflict between the public's
political views and the Kennedys'.

Lots of politicans--before and after--fooled around with staffers,
interns, and young women in general. So that doesn't count for much.
(Runs in the Kennedy blood, so to speak.) As for her death, I think
most view that as an unfortunate event, a tragedy, if you will. (The
conspiracy fanatics may argue that it was intentional...and they may
argue that Vince Foster was murdered. Maybe so. But, like it or not,
the general consensus is that her death was an accident.)

The real issue is the way Teddy handled it--his attempted cover-up.
That reflected incredibly poor judgment, and I think many people
realize that. Mary Joe's death ended Teddy's aspirations for the
presidency and significantly limited his influence on the national
stage. Since then, he's studied hard, built up a huge amount of
seniority, toned down his act (especially with his new wife), and
become an "elder statesman."

His judgment is still suspect, but many in Massachusetts see Teddy as
the end of a Massachusetts dynasty, politically in tune with their
feelings, and a power in the Senate. They're willing to overlook
affairs, and they're willing to accept that Mary Joe's death was an
accident. Final point: Many of today's voters weren't even born (or
were still in diapers) when the incident occurred. Many probably don't
even know about it. And that's why he keeps getting re-elected.

Sen. Edward Kennedy suffered the losses by assassins of his two older
brothers. Had JFK lived, his admin. might have accomplished a great
deal in two terms. RFK was well positioned in 1968 to be nominated by
the Democrats and he might very well have defeated Nixon. Had he been
elected president the Vietnam War would have ended sooner and the
civil rights movement might have been reinvigorated after the murder
of Martin Luther King. He is the last link to an era that was
destroyed by violence.

I concur with the commenter that his behavior in the aftermath did
limit his political zenith---winning the presidency was now out of the
question.

Home to Harvard, voters of his state evidently separate his espoused
public policy positions from his personal practice behaviors
("character" in corporate media code).

Finally, incumbants in the House and Senate have an overwhelmingly
high probablity of re-election.

from 1998 results:

http://www.commondreams.org/pressreleases/Nov%2098/110498h.htm

"Incumbents were by far the biggest winners....[Senate] Democratic
incumbent Harry Reid wins in Nevada, the rate will rise to 90.0
percent; if he loses it will fall to 86.7 percent."

"In the House of Representatives, only six incumbents out of 401 lost
at the polls on Tuesday.....House reelection rate was 98.3 percent -
the highest rate since 1988 and one of the highest this century."

From 2002 results:

http://usinfo.state.gov/products/pubs/election04/congress.htm

"In 2002, 398 House members ran for reelection, and only 16 were
defeated, while a mere three out of 26 senators running for reelection
lost. With a reelection rate of 88 percent for the Senate and 96
percent for the House, it is fair to say that congressional elections
are not just candidate centered but incumbent centered as well."

House results may be further affected by a gerrymandering factor:
http://www.pbs.org/pov/pov2004/lastmanstanding/special_toobin.html


From 2004 results:
http://www.townhall.com/election2004/senate_details.html

A quick scan of the chart apparently show that only one (1) Senate
incumbent seeking re-election lost, that being Daschle (D) of South
Dakota but he was the subject of some strategic efforts to oust the
Democrats' Senate Leader.