I want to save my sms messages which are in my phone memory to a computer...

you have to use the "sync" function. it should be available with the installation disc of your phone. anyways, using the "sync" function will copy all the data to your computer (msgs and contacts).

I hate when People dont tell their phone models..

use Nokia PC Suite to sync SMS with PC (Nokia Phone)..
use My Phone Explorer to sync SMS with PC (SonyEricsson Phones)..
use Motorola PhoneTools to sync SMS with PC (Motorola Phones)..
use PC Studio to sync SMS with PC (Samsung phones)..

If your phone is Sony Ericsson try downloading MyPhone Explorer application. Download it from here: http://www.fjsoft.at/en/downloads.php . With this application you can manage your phone memory, messages, calls. When it synchronizes with your phone it saves your SMS (and other info) in PC memory.