Cool thread. I'm a big fan of Get Carter (1971) as well as Pulp (1972) which almost seems like a parody companion piece. Incidentally, George Martin did the score for Pulp, which is also great.
I also really like Cloudburst (1951) and was surprised to find it mentioned.
Others I enjoy:
Brighton Rock (1947)
Cul-de-Sac (1966)
Mona Lisa (1986)
The Long Good Friday (1980)
Sexy Beast (2001)
Don't know if Peeping Tom (1960) falls into the Crime or Horror genre, but whatever it is , I love it.