Yes, take a look at Microsoft.SharePoint.WebPartPages.WebPartStorageAttribute in
the SDK, specifically the "Creating a Web Part with Custom Properties" example.

I am trying the same thing but it is not saving the changes for a
particular user. What is happenning is that as soon as soon as any
user changes the property it gets changed for all users, though I
have specified the webpart.storage property as storage.personal.

Are you using authenticated or anonymous users? Is the portal setup for
anonymous access?

I have disabled anonymous access on my portal site...
And every user  of my portal site falls under a site group...
But still the problem remains the same... Changes done at last are
saved....
I wanted  to know that everytime when the webpart  is rendered, are the
properties retrieved form the database???
I also tried explicitly saving the properties  by
using "saveproperties" property but still result was the same...
I want to know that is the webpart rendered from the cache or from
database after retrieving the various properties..???

A couple more questions - are personalization rights granted for each user, and
are they using the web part in the shared or personal view of the page?

The users  are modifying the webpart  in a shared view. How to grant
personalization rights ????
One more question is that can a site admin target a custom  webpart to
all the users of the site on their my site???

Personalization is a right like any other - you just assign it to a site group
or role, then add the users  to that group or role. I just answered the other
question in a separate email.