Adding new methods to GenericDataAccess
First of all, there is no need to write a generic data access class.  Use the Data Access Application Block.  It gives you everything you need to access a database.  Why reinvent the wheel.  You can even download the source code to this if you want to see how Microsoft does it.

Having said that, if you are doing this just as an exercise then I see a couple things...

I am not a big fan of static classes (except for possibly simple "function" classes, classes which provide generic functions such as a function to convert unix timestamp to datetime).  Making classes static makes it more difficult to unit test.  

Along these lines of unit testing I would also recommend you implement an interface so you could can make unit testing easier through IOC / dependency injection

Your methods should only do one thing.  Adding too much functionality into each method limits the flexibility of the caller.  You should have a method that creates a connection, another that creates a command, and another that executes the command.  Example, I would not open and close my connections within the "Execute..." methods because what if the caller wants to open the connection so they can execute multiple commands in the same connection.  If you want to add methods that do multiple things then they should be separate from your generic data access class, and they should call your generic data access methods.

I do not see anything to handle transactions.  This would be something you would want to add.