They typically hold them at ski resorts, so the way the course usually gets laid out is run up ski slope, obstacle, run down ski slope, obstacle and then repeat for ~9 more miles. Most of the obstacles are what you would expect for a mud run (just more of them), but there are a few notable exceptions: the fire obstacle, the water obstacles and the electroshock obstacle. 

The water obstacles are deliberately filled with ice where possible to make them as uncomfortable as they can: it's so cold it just steals the air right out of your lungs and makes your head hurt when you submerge. It also stiffens your muscles right up and makes it extremely difficult to start running again and conquer obstacles. However, this is exactly what you need to do in order to get your body temp back up. 

The fire obstacle, at least for the course I ran, wasn't difficult because of the flames, but just the sheer volume of smoke, which made it nearly impossible to see where you were going and even more difficult to breathe. You're already winded at this point in the race so coughing your way through the smoke is a rough experience. 

The electroshock obstacle is unique to the Tough Mudder and probably one of the most intimidating. Just prior to it you pass through a firehose spray so you're all wet and a good electrical conductor. You basically just make yourself into a wedge and charge through to the other side as quick as you can. I did get zapped on my ear, but the current wasn't nearly as strong as I would have expected: it felt like someone slapped me across the face.

At the finish they give you the coveted orange headband and a frosty beer: probably the most enjoyable beer I've had in my life. 

There's a great spirit of camaraderie with all the competitors. At nearly every obstacle there are helping hands and supportive shouts from your fellow runners. A few obstacles absolutely require assistance to complete and it's great to look up and see a hand thrust down to pull you up. 

A great experience and one I'd certainly do again.