19 – the actual number of berachos in weekday Shmone Esrai
perek 19 of Tehillim is the first perek of Tehillim that we say in pesukai d’zimra of Shabbos and Yom Tov that is not included during the week.
19 – the number of years in the cycle of leap years and non-leap years in the Hebrew calendar. see http://rabbikaganoff.com/archives/1675 for more info.
18 – perek of Tehillim where Dovid praised HaShem for saving him from Shaul