I love classic movies. Here are some suggestions, depending on what you're looking for:
Suspense: I love Rear Window, which stars Jimmy Stewart and is an Alfred Hitchcock classic murder mystery about a man who believes he has witnessed a murder from his rear window. Also a favorite of mine is Charade, starring Audrey Hepburne, Cary Grant, and Walter Matthau; this movie has a great blend of romance, plot twists, and action.
Musicals: Starring Walter Matthau as the stingy curmudgeon looking for a bride and Barbra Streisand as the cunning matchmaker, Hello, Dolly! is a hilarious and fun musical with a great combination of comedy and memorable songs. My Fair Lady also ranks up there as one of my all-time favorite movies ever.
Comedy: One of the best that I can recommend is the classic screwball comedy, Bringing Up Baby; Katherine Hepburn and Cary Grant are comedic gold in this movie. It's very quick-witted and tongue-and-cheek!