Careful. Your first two solutions will happily remove a correct, lone .html. Rather, you should replace multiple occurences with a single one, as you (almost) did in your oneliner: 
# perl rename
rename 's/(?:\.html){2,}$/.html/' *.html

[download]
# unix rename
rename .html.html .html *.html

[download]
Your oneliner can be shortened by not checking if a substitution will be successful first; the substitution simply fails if no match is found. Untested: 
# perl oneliner
perl -e '-f && ($a = $_) =~ s/(?:\.html){2,}$/.html/ && -e $new ? warn
+ $_ : rename $_, $new for @ARGV' *.html

[download]

Makeshifts last the longest.

In reply to Re^2: help on stripping out extra extensions by Aristotle
in thread help on stripping out extra extensions by Anonymous Monk

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