The Castle Complex was partially destroyed by Teutonic Knights in 1390, and then after the Battle of Vilnius in 1655 many of the buildings became ruins. During partitions it was still being demolished and soon the Gediminas' Tower became the last part of it that was left.
It's important place and also a symbol -- Lithuanian flag was re-hoisted there on October 7, 1988, during the independence movement. This Tower is also depicted on the litas (Lithuanian currency), and is often mentioned in Lithuanian poems and folk songs.
[2011 edit:] If I was making this account now I'd rather choose a username that'd have more to do with the character than the country, but I got pretty used to it by now ;o;