Another route preferred by travellers is Bucharest to Istanbul. Things have changed a little in this respect and nowadays there is a direct train to there and also buses. There is a catch though if you plan to take the train. The info below is updated today, the 18th of April 2013.
Train: there is one train a day, it leaves at 12:30 and it gets to Istanbul at 7:50. It costs 236 lei for a bed in a 6 bed sleeper. The only thing is that the train will take you to one point (30 km before Istanbul) and from there you will change to a bus. The price quoted above includes both the train and the bus to destination. For more information and prices, you can call the train station or the train ticket agency, info here.
Bus: there are several companies that leave for Istanbul regularly, they are faster and cheaper than the train. There is Ortadogu, they leave at 16:00 everyday except for Saturdays. One way to Istanbul costs 160 lei. There is also Marina, they leave at 17:00 everyday except for saturday. Same price. Contact info for these companies on ourTravel links page.
Again, the same warning applies: this information is valid right now, in summer it might change in terms of prices and times, but not much.