Given a string find the substring which appears most often
Perl, 99 (+1) bytes

$_=$;{(sort%;)[m{(.+).*\1(?{$;{$;x$+=~y///c.1x@{[/$+/g]}.2x$+[1]}=$+})^}]}
||"No substrings repeat."


Requires a -p command line switch.

For each repeated substring a hash entry is created, such that the largest substring, repeated the most times, with the earliest position is guaranteed to be the smallest key in the hash. The hash is then sorted, and the corresponding value for the smallest key is output.

Sample Usage:

$ echo 123456 | perl -p repeated-substring.pl
No substrings repeat.

$ echo 12121 | perl -p repeated-substring.pl
12

$ echo 99999999 | perl -p repeated-substring.pl
9999

$ echo 321321788788788 | perl -p repeated-substring.pl
788

$ echo 12012112299999999 | perl -p repeated-substring.pl
9999

$ echo 56698853211564788954126162561664412355899990001212345 | perl -p repeated-substring.pl
412