The content type of the source file will define what the best file type to supply would be.

Vector EPS, TIFF or PDF are fairly compatible file types - in so much as they can opened in a wide variety of applications and none are native to one package - I havn't used Corel for a long time but I know for sure that you an open EPS, PDF & TIFF files using Freehand, Illustrator, Photoshop, Fireworks ... Of course if a user oped a vector graphic in a raster package it will render the graphic - and the vector information would be lost...

Can you give a little more detail on what the users will do with the files once they download them?

I once downloaded a PSD file from a T-shirt site that contained numerous layers - each layer contained a different colour T so you create a design on the top layer and apply the graphic to a choice of different tee colours - quite a good system in that case - it did make a big assumption about a users ability with Photoshop mind you...

The files are basic designs for a paper product. Once the customer downloads them they will customize the design and email the final design back to the company.

There is also a compression algorythm for recent Corel Draw files. Fortunately, you can save CPT files as PSD files with all layers and channels intact, while you can save Corel Draw files as Illustrator .AI files without any problems.

Then your users can use them. But be weary of the colour differences when doing such a conversion.