There is basically only two ways to get from Dushanbe to Khorog: fly or drive. Obviously, flying is the fastest of the two options, taking about an hour (as compared to the minimum 17 hour car ride). Each option has their pros and cons, though.
The road route is brutal, but beautiful. The route is at least 17 hours; guidebooks and others say it averages 22 hours. If you leave Dushanbe around 7am (from the car park near the airport), you can be in Khorog by around midnight. Shared taxis/vans will do the first stage in one long day, which is brutally uncomfortable (unless you score the front seat), though if you hire your own car/driver you can break the journey into two days (stopping in Kalaikhum). Along the route, you will pass the Rogun dam, many small villages, and a high pass where the temperature drops considerably (and gets closed in the winter months due to snow). Most of the ride, though, is along one of most bone-jarring bumpy roads you will ever ride, preventing your car from ever breaking the 20mph barrier.
I was able to hire my driver with the help of a cousin who runs the Pamir Lodge. After meeting me at the airport at 3:30am (after he spent the earlier part of the evening clubbing with some friends), we spent a few hours in the airport lounge talking while his friends slept-off their night of clubbing. At 7am, after deciding I did not want to risk missing the flight to Khorog, this cousin took me to the car park near the airport, and told me to stay inside the taxi we took there while he found me a ride. For about $50, you can get a seat in a shared taxi. In no time we found people offering just that: a shared seat in a car. But, just when I felt I would take that option, he found a friend who had a whole car and would let me ride for $50...with no other passengers. So, I got the front seat and basically a personal driver to take me the whole way. In addition to the money he needed for the gas, I paid for his meals, too. I quickly thanked the cousin for his troubles, and then the driver and I stopped at a gas station and grocery store to grab some food for the ride. We were then off.
After you reach Kalaikhum, the remainder of the route follows the river separating Tajikistan and Afghanistan. Views into Afghanistan are spectacular, with numerous villages that have probably not changed in thousands of years. The villages on the Afghan side are all connected by dirt paths, often seen clinging to the sides of mountains and cliffs. While we sped along in our car on a decent road, it felt like we were looking back in time at the Afghan side, with people walking along dirt trails with their donkey carts and such. It was truly amazing.
If you stop in Kalaikhum, though, you will definitely see the amazing Afghan villages when you travel during the day on day 2. However, if you decide to make the trip in a single day from Dushanbe, you will totally miss these villages. I saw the villages on my return from Khorog to Dushanbe, but on my way there I could only see the river and cliffs from the full moon that night.
One thing to note about the route between Kalaikhum and Khorog, as it follows the Afghan border the entire time: the road was mined in the past. You will see signs that areas along the road have been cleared of mines. But, you can never be too sure if they are all gone. So, if you stop to take a break, be careful where you step.
The plane route is (obviously) the quickest. However, it is also the hardest to make happen. Each morning there is a single flight from Dushanbe to the Tajikistan town of Khorog. The flight is only about an hour, and leaves at 8am each day. Tickets go on sale at 7am the day of the flight only, and the flight happens only if the weather is good and enough people want to fly that day. If the flight the previous day was cancelled, ticket holders from that flight will already be ahead of you for the flight. I did not make the flight, as the flight the day before had been cancelled, and the weather was not ideal. Based on other travelers' experiences, the flight is spectacular, and gets you up close and personal with the peaks of the mountains. There are YouTube videos of the flight. The disadvantage of the flight option is that you totally miss the unique and spectacular villages on the Afghan side.
Side note: though the plane route seems to come dangerously close to the mountains, there has never been an accident on the route. The only time a plane crashed was when it was shot down from the Afghan side. Happy travels!