Bill & Ted's Excellent Adventure (1989)
Reeves didn't start out playing cool characters in designer shades or cops trying to stop runaway buses. His breakthrough in Hollywood was this comedy, which appears to be goofy at first but actually makes for interesting viewing. Reeves plays Ted, a dumb high school kid who can't graduate with his best friend, Bill, unless they pass a history project. With the help of a guy from the future who comes through a phone box, the pair travel through time in order to get their high school certificates - and save their metal band from breaking up.
My Own Private Idaho (1991)
Although it was never a box-office success, it's still one of his most talked-about films. The late River Phoenix and Reeves became instant Hollywood heart-throbs after starring in this Gus Van Sant movie loosely based on Henry IV, about a pair of hustlers in Portland who might or might not have fallen in love. Phoenix, with perhaps his best performance, won the best actor award at Venice in the same year. As for Reeves, this film and Point Break of the same year (he plays an FBI rookie who has to go undercover as a surfer) established his name as a hunk in the business.
Speed (1994)
The plot might sound ridiculous at first (stopping a runaway bus?), but this Jan de Bont-directed film turns out to be one the most exhilarating in years. Reeves plays a Swat team member who has to save the passengers on a bus rigged with a bomb that will detonate if its speed goes below 50 mph - or anyone tries to get off.