Many people think of the Kaddish as a mourner's prayer, because the oldest son is obligated to recite it for a certain period after a parent's death, but in fact it is much broader than that. Another important prayer is Aleinu, which is recited at or near the end of every service. It also praises G-d . On that day, the L-rd will be One and His Name will be One. On certain holidays, we also recite Hallel, which consists of Psalms 113-118.
Many holidays have special additions to the liturgy.
See Yom Kippur Liturgy for additions related to that holiday. There are a few other things, but that's a pretty good idea of what's involved. This is based on the Ashkenazic service, but the Sephardic service has a very similar structure. They use different music, and have a few variations in choice of psalms, hymns, and prayers. See Ashkenazic and Sephardic Jews for more information.