Answer: No.

Silverlight does not have offline database support neither does Flash. The offline database support is most likely a confusion between Adobe Flash Player and Adobe AIR.

Silverlight however does have what I call "uber cookies" (yes that's a Barnes technical term) where you have the ability to store packets of data in what we call lsolated Storage. Isolated Storage Provides safe access from the Silverlight client to the local machine's file system. Enables local storage and caching of data isolated to a particular user.

Do you have a Silverlight vs Flash Question that you want answered? Please send me a note via this form and I'll help clear the air around both technologies.

Examples in the wild:

• Flickr’s Multi-Picture Uploader done in SilverLight
• Silverlight Tutorial - Using Isolated Storage
• How to: Use Isolated Storage with .NET Framework Silverlight
• Silverlight Isolated Storage

Things to Note:

• Both technologies have the ability to talk to server-side solutions using various methods (I'll cover off later) and this is how one is able to send/receive information from a database.
  
• Flash has a similar concept called LocalShared Objects, where you can also save data per user to a persons hard drive.
  
• Both technologies are housed within a "Sandbox" which whilst allows the runtimes to save data to a persons hard-drive, they however cannot escape the sandbox due to security permissions.

Dear Commenter,
At times the Silverlight vs Flash discussion (no matter the intent) can at times turn into a heated discussion. In the interest of simply preserving the facts I may edit the comments left on this of post to ensure that the we stay on topic and true to the intent of this post - clearing up misconceptions. If you have evidence that differs from the above, I will be more than happy to make changes and source the author.

Questions found in Comments

Q. Is it per domain or per page? And if someone visits my site in IE and I save something in Isolated Storage will they be able to retrieve that information if they visit using the FireFox browser? - John

A. It’s currently per application’s source domain. Yes you can share persist data between browsers as they all point to the one area (within the secure sandbox). This will allow folks to share “Form values” - for example - between two browsers, so in the event UserA leaves for whatever reason in BrowserA, they can resume the data in BrowserB.

There are likely to be some adjustments to IsoStore in Silverlight 2.0. Keep an eye on Silverlight.NET’s blogs for more information as it’s announced.