"Dirtex" is great. I've been using it for 15 years on stainless, windows, granite, and bathroom sinks, and more. It's the only thing I've tried that doesn't streak. You can get it below on Amazon, or it can often be found at paint stores such as "Porter" and "Ben Moore". I buy 6 cans at a time and keep them all over my house. Jeweler's actually use it.
Be careful not to breath it....as with most cleaners.

Don't buy it at Ace Hardware...they charge too much.

You might want to read the reviews on Amazon:

http://www.amazon.com/Savogran-10761-Dirtex-Cleaner/dp/B000BQL2FU/ref=sr_1_1?ie=UTF8&s=hpc&qid=1267160418&sr=8-1

It is always a good idea to see what the manufacturer suggests for cleaning a product. Here is what Dupont says about Corian:

Soapy water, ammonia based cleaners (not window cleaners as they can leave a waxy build up that may dull the surface) or commercially available solid surface cleaners will remove most dirt and residue from all types of finishes. Stubborn residue will require a little stronger cleaner.

Follow the recommendations below to properly clean your countertop and sink.

Experience has shown that a film builds up on the surface if water is left to dry on the countertop. This film will dull the look of the countertop making the finish appear blotchy and uneven. To prevent build up of the film, it is very important to wipe the countertop completely dry after spills and cleaning.

The Dirtex mentioned above should do fine because it has ammonia in it. But rinsing and drying the counter is what's going to make the difference.

Here is a link that might be useful: Dupont Corian

I use Cinch spray (made by Spic n Span) , but wipe it off quickly as it tends to leave streaks. I have Corian countertops in my kitchen.