Huge, Lots of fun cruising runs, Family friendly, and Fun town.
Nothing overly challenging, & expensive.
Fantastic resort. Combined with the Italian terrain of Bruil-Cervinia and Valtournenche, it is an enormous alpine area that is completely connected. You can ski from the Rothorn Paradise to the Matterhorn Glacier Paradise, over to the Italian side and all the way to the Schwartzsee Paradise without ever going all the way back to town/base area. The on-piste terrain is moderately challenging. The Stockhorn area is the most notable exception, but it is more of a mogul field than off-piste terrain. There are obviously some extremely challenging lines off-piste, but the existance of crevases, cliffs and the glacier makes hiring a guide a necessity. If you are looking for challenging on-piste terrain, I would head to Chamonix, Courmayeur, or St. Anton, but for me part of the overall experience of a European ski resort is experiencing the culture.
Zermatt is wonderfully vibrant town. Downtown is filled with bustling shops, exquisite restaurants and lively pubs. The town is fun, but bring your cash as it is truely the Aspen of Europe pricewise. The vacationers come to Zermatt to eat well, and they pay heavily to do it. Despite a favorable exchange rate for Americans, the price of goods are still very high in Switzerland. The cheapest small margarita pizza that I found was about $17. A pint of lager is going to cost you $5-$7, but the dinner crouds are more likely to buy a bottle of wine. Overall, a very wonderful alpine town.
In a nut shell: Take your family to Zermatt, but there are more challenging European choices for you and your diehard ski buddies.