Now, about that hotel...
Don't get too carried away there, buddy -- you're not getting a free night at the Burj al Arab. The hotels are along the lines of ones US airlines use to put passengers up when flights are cancelled. That is, reasonable, comfortable hotels within a short drive from the airport.
But, hey, free is free, and you can still take full advantage of your quick trip. Many of the hotels offer late-night tours of the city. Also, Dubai has a fantastic Metro system that can get you from the airport to pretty much any attraction. Cabs are surprisingly affordable, so heading to an indoor ski slope or the Palm Islands won't demolish your bank account. Past that, if you opt to eat $20 hamburgers on Jumeirah Beach, that's on you.
So if you're planning a big, round-the-world flight this year, and you see an option for an Emirates flight with a day-long layover, don't immediately assume it's adding $400 to the cost of your trip. Look at it as a chance to explore one of the most dynamic cities in the world on your airline's dime.