If you like Music for 18 Musicians then you should try other Steve Reich music especially directly from the same era.
Some suggestions are:
Music for Mallet Instruments Voices and Organ - a more laid back feel than 18 Musicians and just 20 minutes in length. Short phrases and chord sequences are doubled, then doubled again, then again, and much like with 18 Musicians the process then reverses. A beautifully calming piece of music.
Six Pianos or Six Marimbas - probably easier to listen to in it's Marimba guise, a busy piece which doesn't provide the change in timbre which like 18 Musicians does, but does give you the chopping and changing rhythms which are instantly recognisable.
Music for a Large Ensemble - very similar indeed to 18 Musicians, a bit like it's older brother but only 15 minutes long. It doesn't have the pulse in the same way as 18 Musicians but does have the vibraphone conductor and uses the "breath" effect in a similar way as well. Tends to be less well known maybe because it is more difficult to perform and is overshadowed by 18 Musicians?
Octet/Eight Lines - the pulse is maintained by pianos rather than traditional tuned percussions instruments. Themes are built up organically from an initial few notes to complex and interweaving melodies in a more complicated way than you find on 18 Musicians. You can tell that this piece is a progression from the ideas on 18 Musicians.
Double Sextet, a composition which won the Pulitzer Prize in 2009. One group of six musicians plays alongside another group of six musicians (or a recording) creating a mind boggling yet wonderfully animated piece of music.
Other Reich classics are Tehillim (hugely uplifting singing of sacred texts) , Music for Pieces of Wood (basic manual phasing, but lots of fun), Proverb (different yet still Steve Reich), Variations for Winds, Strings and Keyboards (one of Reich's few pieces for Orchestra), and Electronic Counterpoint (probably the most easy listening of all Reich's music, for electric guitar, including the pulses again!)