Movie and TV Recommendations (UK). This is obviously one of a stable of products, given that I've just taken a look at the games version of this app. This works in exactly the same way; just type in a film that you like and you are presented with a variety of suggestions. I tried a few examples myself and overall I was very satisfied with the results I got.
HelloMovies is a straightforward resource. Search for a movie and get a summary, rating, cast and crew details and similar movies. Not entirely sure about the latter though - a search for Casablanca also suggests Count of Monte Cristo, Pride and Prejudice, Shakespeare in Love and the Great Escape. It may give you some ideas of things to watch though, based on your favourites.
Nanocrowd. This is very clever, and I like it. It's a discovery engine rather than
a search engine though. Simply type in a film/actor/director that you
like, and Nanocrowd will attempt to find others that you like.
Matchmine "lets you discover a whole new world of music, movies, video and other
cool stuff that match the tastes of the one-of-kind inner you. How?
Your MatchKey™ lets you capture your personal interests and media
preferences and take them with you to get what you want across a
growing list of partner websites and applications. Creating your
MatchKey is easy, anonymous, free and you can start using it right away
to find media you’ll love."