If you mean in a career, nobody has remotely approached it. His .366 LIFETIME batting average has been bested for ONE YEAR in either league only twelve times in the last fifty years.
Cobb never held the record for highest batting average in a season. It was set by Hugh Duffy at .440 in 1894, and it is inconceivable to me that it will ever be broken.
Joe Mauer of the 2009 Minnesota Twins set the record for highest batting average by a catcher with .365. He broke the record held jointly by Bill Dickey of the 1936 New York Yankees and Mike Piazza of the 1997 Los Angeles Dodgers at .362. Joe Mauer broke another Joe's record. Joe Torre batted .363 in 1971 enroute to winning the M.V.P. Not Mike Piazza's .362.
When Tebow did his in 2010 they said he either broke or tied the record for Quarterbacks.
Her first record was the highest altitude for women . This was in 1921 in her 'Canary'.
Sachin Tendulkar Broke Brian Lara's Record of highest runs 11953 & has currently scored 12917+* Runs.
When Bob Beamon broke hte world record, he was 1.5 fett above the ground.
Curlin. This horse broke Cigars record of 12 years in September 2008 in the Jockey Gold Cup. This is the highest earning horse in the USA
Barry Bonds broke the record in the 20 century.
He broke his own 100m record, the 200m record of Michael Johnson and the 4x100mR record of the USA.
UT's Ricky Williams broke the record (although he does not hold the current record).
Lionel broke the country record in scoring the perfect goal at the soccer match