What exactly are good quality database solutions that support Silverlight and therefore are solid for any small-medium traffic website

Simple to useOrHandle is an extremely strong plus

edit: Didn't remember to say the database must be very smartphone-friendly, it must have the ability to use products on iOS, Android, and Home windows Phone 7

It is dependent on which you term small-medium. I'd say SQL Server Express should meet your requirements.

It's free, however your database size can't be a lot more than 10 GB. Additionally, it limits the assets you can use in the server.

http://www.microsoft.com/express/Database/Default.aspx

Silverlight isn't certain to a database. Every database open to ADO.Internet is functional within .Internet. MSSQL Express is a great solution (particularly in .Internet env) in addition to every other like MySQL.

SQL Server Express is a nice apparent choice. Combines perfectly, a lot of top class documentation, very reliable, good management studio, upgradeable to more effective versions etc.

Thinking about your edit, it seems to become a home windows phone 7 application that you are will make, which you would like the database saved on the telephone (instead of hooking up to an online datasource). For the reason that situation, you might like to have a look at SQL Server 2008 Compact.

Scott Hanselman comes with an article about using EF Code First with SQL Server Compact (His solution doesn't particularly include Silverlight, however it works likewise iirc) here.