Sheesh! Too much brake talk!
I don`t disagree with anything already posted in this thread, but there are a lot of red herrings. In the unlikely event that your brakes and levers aren`t compatible, there are a few cheap and easy fixes that will take care of the problem.

There are a number of "standard" clamp diameters for bars (where the stem clamps the bar) and , as far as I know, two diameters for where the brake or shift levers clamp. Finding the correct combos shouldn`t be too much trouble, but since there are differences I`d just go to a local shop where you can physically compare everything and make sure it fits together before you buy it and have it shipped. The guys at the shop should also be able to tell you at a glance what "pull" you need for you current brakes.

The biggest obstacle to putting dropbars on a mountain bike is finding a stem that lets you get your bars in a comfortable position. Since mtbs generally have longer and lower top tubes (after all, they`re designed to be used with flat bars) than "road" bikes, chances are you`ll need a different stem anyway- probably one that`s higher and has a shorter reach. The easiest way to get yourself set up is at a shop with a good stock of stems in stock so you can try as many as it takes to get your bars where you need them. That`s a piece of cake if the stems have removeable front plate as opposed to the single bolt style that require you to strip a shifter and brake lever off your bars for each attempt. As mentioned above, you can use an adaptor to fit a modern stem intended for threadless systems, or you can use a taller quill style- either way will do the trick.

Dropbars also come in a variety of shapes and sizes. If you`re comfortable with one of the short reach bars (sometimes labled as "cyclocross" bars or "compact" drops), you`ll have a little easier time finding a stem that works for you. Again, your LBS is the place to look. You can probably test ride bikes that have different bar styles to see which ones you like best and buy a similarly sized and shaped bar. I order a lot of stuff from online vendors, but this is a prime example of a project that will be much easier with the help of a well stocked LBS.