The thought of grouted tile in a food preparation area has always put a chill down my spine but I can see no reason why you can't put tile on Corian if you choose the right glue. It's best to use large floor tiles and 1/8" joints if possible. I would use a pro since the edges will be more difficult.

If you like the look of stone or cement counter tops there are two products made that would adhere to the corian and completely change the look. I saw the concrete version in a magazine- they used a product called featherlite I think. It covered old laminate countertops in both the kitchen and the bathroom they even did the undermount sink in the bathroom. It then had to be sealed with a clear sealer to keep out water and they said it was food safe and would last.
The other technique, more of a stone look, was on "Design on a dime" show which I think is HGTV network. They tinted the surface material to the color stone effect they were looking for and again covered old laminate countertop in kitchen. It took three steps to complete. If you like either of these ideas I can find the link to the show and the materials- I am sure I bookmarked them.

That sounds interesting -- would love to see the link!

-Melissa

Here is the link to the Modern Masters Skim Stone website. This is the product I saw demo on "Design on a Dime" show for a laminate countertop.

"SkimStone® Decorative Floor Finish (Hybridized Portland Cement) is an innovative trowel-applied interior/exterior decorative finish for floors, laminate and ceramic countertops. A three-coat application creates a unique textured appearance that transforms concrete floors and countertops into beautiful design element.

They even have tech sheets on website.

Here is the episode I saw
http://www.hgtv.com/hgtv/dc_design_kitchen/article/0,1793,HGTV_3375_5455954,00.html

"Fontana takes on the worn, cracked countertops with a skim stone refinishing product. He spreads a bonding primer on the countertop with a trowel (or with a brush on the bullnose sections). After two coats of primer, the color coat goes on. Fontana has chosen a Tuscan olive green, and the finish is a raw, stone-like texture, which adds a natural, organic touch to the kitchen. Finally, a food-safe sealer is applied with a rag, and it brings out the rich green tones. "
They used plastic wrap to get a smooth bullnose edge and it didn't look that hard.

Let me know if you try it!

Here is a link that might be useful: Modern Stone Masters

Tiling counters was very popular back in the 80's. It took a while before problems were discovered. Discoloring of the grout around the sinks and cooktops were the most common. This occurred to the most anal people who would seal the area on a regular basis. Most people are not that industrious and the counter would look like crap within a year or two. Epoxy grouts will delay, but not eliminate the issue.
Ron