A wide range of music is available for the wedding ceremony.  Some popular alternatives include:

Brass Quintet

Celtic duo (hammer dulcimer, harp, lap dulcimer, guitar, violin, harmony vocals)

Celtic/variety duo - Hammer dulcimer/guitar(s)/violin/vocals

Celtic trio

Celtic quartet

Ethnic music groups (Jewish, etc)

Flute duo/quartet

Guitar - fingerstyle/variety

Guitar - classical

Harp (concert or folk)

Harp and flute

Mixed trio - piano, cello and flute

Mixed trio - flute, violin and cello

Piano - any style

Soloists of all types

Stringed ensembles 

Woodwind Quintet

.....and more!