The most obvious thing would be to remove the previous value section from the appropriate template in the AlertTemplates.xml file. However, I cannot advise strongly enough to leave this alone. Customizing SharePoint alerts is both a black art and a Pandora's Box. It takes a fair amount of work to open it and once you do you regret it for as long as anyone remembers that you touched it.
However, if you insist on customizing them, then read this article on MSDN first to get a good understanding of what you are diving into.
My recollection is that the basic approach would be:
- Copy your alertttemplate.xml file to another name (NEVER modify the original!!!)
- Modify your new file to exclude the old values from the notification.
- register your new template file
- associate your template file with the list in question
- if you changed your template name, delete and recreate all existing alerts for the list.
- begin testing the various conditions that trigger alerts. Bear in mind that list settings such as versioning and mandatory checkin/out will change what types of alerts are generated.
Oh, and don't forget that Alerts come in two variants: Immediate and Digest and you will have to fix both types. Naturally, they are different and you will come to loathe testing digest alerts in less than 3 minutes - time it. (ok, perhaps 'loathe' is too strong as that doesn't set in until around the 15 minute mark - 'dislike' maybe?)
One last point - if someone asked you for an estimate for this work, triple it now before starting on the work and be sure to include maintenance and troubleshooting time once the feature is deployed.
You have been warned.