Denver has really changed for the better over the years. It's no longer the "cow town" that it was always known as. There are so many positive aspects of Denver that it's hard to list just one thing.
Downtown Denver has very much changed over the years and offers a nice place to wine and dine. In addition, there are some really fun areas that have gained popularity over the years such as "The Highlands", "Lowry", "Stapleton", "Old Towne Arvada", "Historic Downtown Littleton", "Belmar" and "The Streets at SouthGlenn" have added some great shopping and dining avenues.
Denver has been voted as one of the top "Sports Cities" in the nation thanks to having so many professional and college teams located in or near Denver. The area really supports each sport and we have a lot of them (football, basketball, baseball, hockey, lacrosse, soccer). Denver offers many museum and cultural events/venues.
The city is large enough to have plenty to do, but not overwhelmingly large. The climate is mild; insects are not much of a problem. Traffic is not bad compared to other large cities.
Finally, I think the easy access to outdoor activities is a real plus. There are plenty of bike trails and parks throughout the city or one can easily go to the "high country" to camp, ski/snowboard, snowmobile, mountain bike, fish, and hunt (and more). It's easy to see why so many people are attracted to the area.