Show creator David Shore stated that the similarities between Dr. House and Sherlock Holmes were intentional, starting with House and the similar sounding Holmes. From there, both House and Holmes solve cases, play instruments, and use drugs (Holmes did coke, if you didn’t know). Also, as a shout-out, House lives in appartment 221B, which is a reference to Holmes’ street address (221B Baker Street).

Other connections include:
Holmes’ sidekick Dr. John Watson lead to Dr. James Wilson in House.
House pilot episode patient Rebecca Adler after Holmes first short story character Irene Adler.
Season 2 gunman nickname “Moriarty.”
and Season 5, a book written by Joseph Bell, which was the inspiration for Conan Doyle to write Sherlock Holmes, was given to House with a note which was signed by “Irene Adler” (see above).

Source: wiki