In order to maintain all your tables and data the way it is, you often require to perform an incremental update for magento, doing it otherwise might make some of your data obsolete. Here is a simple step by step guide to perform magento incremental update:
First you have to back up your existing database. You will need it later while importing the data and tables to your new database.
To create backup you can use PHPMyAdmin or any other database export script of your choice. Other way to get backup of large database is using commandline. Mysqldump is the default mysql utility to create backup. Following is the example
mysqldump -h localhost -u database user -pPassword database name > /path/to/dumfile.sql
Next you have to check the version of your current installation, you can check it in footer section of your admin panel or you can check it in code in app/Mage.php file getVersion() function.
Once you have identified the current version, go to Magento download page and click on archive tab. Click on Get next stable version, lets say your current version was 126.96.36.199 and the next stable version is 188.8.131.52, so you download that version and install it.
Here is the url to download the 184.108.40.206 version:
If you are trying to update from a newer version here are the remaining URLs that can be used to download the latest version:
Now import the DB backup you created earlier to your new Database. To import database you can directly enter the query if you have access or you can use the below in command line:
mysql -h localhost -u dbuser -pPassword newdatabase < /path/to/dump.sql
Once imported, extract the database and install it on new database.
By the end of this, you have upgraded your magento installation to 220.127.116.11, then find the next stable version and repeat from step 4 to step 6. Keep on repeating the process till you have the latest version of magento installed.
After upgrade copy the following files and folders from original site to new installation
app/code/community/ for custom installed extensions
media/ for copying images of products and categories