I'm not for sure but there seem to be prayers to show one's ahava (love), shevach (praise) and hoda'a (thanksgiving). There seem to be prayers about techina (supplication), bekasha (beseech, request). And there are prayers like vidui (confession), teshuvah (repentance)... and probably there are more forms of prayer.
But what i would like to know; because prayer these days (at least in the world and other religions) seems to be about asking; what is it that one can pray for (except from the things mentioned)? - things like peace, personal needs, etc?