Current showtimes are available from Yahoo and IMDb. Only major theaters are available here, so you may want to try another more general entertainment site for obscure venues (e.g. in DC, the French Embassy, the National Gallery, and the Hirshhorn each have pseudo-weekly high-quality film series) and repertory houses.
To find a movie to rent, try one of Yahoo's list of personal preference predictors (I found the MovieCritic site most helpful), which ask you to rate several movies and then match you with other individuals in their database who have similar preferences to find other movies you might like. The more movies you rate, the more accurate the predictions.
Amazon and IMDb have lists of award-winners (Oscar, Cannes, Venice, etc.), the AFI top-100 lists, and user ratings.
To find info on a particular film, check out:

An exhaustive movie database (with complete cast and crew):
The industry standard:
The industry database:
The insider gossip:
Bright bulbs:
The female perspective:

Some of my favorite directors are: Martin Scorsese, Howard Hawks, Orson Welles, Elia Kazan, Ridley Scott, Alan Rudolph, Jonathan Demme, Alfred Hitchcock, Ang Lee, Mike Leigh, Spike Lee, Wes Anderson, Paul Anderson, David O. Russell, Aki Kaurismäki, Ingmar Bergman, Jane Campion, François Truffaut, Jean-Luc Godard, Jacques Rivette, Vittorio de Sica, Michelangelo Antonioni, Bernardo Bertolucci
My favorite films are listed here, in chronological order.
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