$query = "SELECT * FROM movielist WHERE genre LIKE '%comedy%' ORDER BY dateadded DESC";
OR
$query = "SELECT * FROM movielist WHERE FIND_IN_SET('comedy', genre) ORDER BY dateadded DESC";
Second one is better in most cases.
Even better, you should use a separate table for facilitating many-to-many relationships.
i.e. New table called 'movies_genres' with two fields - movie_id and genre_id (both indexed foreign keys). Every time you add a new genre to a movie or a new movie to a genre, add an entry to this table.
To find all movies belonging to a particular genre:
SELECT movies.*
FROM movies
JOIN movies_genres
ON movies_genres.movie_id = movies.id
JOIN genres
ON movies_genres.genre_id = genres.id
WHERE genres.name = 'comedy'
To find all genres belonging to a particular movie:
SELECT genres.*
FROM genres
JOIN movies_genres
ON movies_genres.genre_id = genres.id
JOIN topics
ON movies_genres.movie_id = movies.id
WHERE movies.name = 'Citizen Kane'