I am using the standard serial display example in arduino ....To my knowledge the Arduino IDE does not come with any serial display example. The reason for this is that there is no standardization among the various vendors of serial LCD adapters. On the other hand virtually every parallel interface uses the defacto standard established by Hitachi with its HD44780U controller and this is the one supported by the Arduino IDE.
However if the string is longer then 16 chars, the rest seems truncated. Also it does not wrap to second line.This is quite normal. You can find an explanation of what is supposed to be happening by following the LCD Addressing link at http://web.alfredstate.edu/weimandn.
Try writing a string of 80 characters and see what happens. Here is a sample sketch for the parallel interface, you will have to modify it for your particular serial setup:
LiquidCrystal lcd(12, 11, 5, 4, 3, 2); // put your pin numbers here
lcd.begin(20, 4); // put your LCD parameters here
for (char i=47; i<127; i++) // send 80 consecutive displayable characters to the LCD
delay(100); // this delay allows you to observe the addressing sequence