I was wondering if there was a monitor that took HDR pictures as input and directly displayed them without mapping them back into LDR space. Is there one?
HDR is about exposure, not about colour space. A monitor has no effect on exposure whatsoever. So your question is incorrectly stated, as there cannot be a "HDR" monitor.
However, there are monitors which can show more colours than the typical sRGB colour space. These are called wide gamut displays. They aren't all that uncommon, the MacBook Pros and the Unibody Macs ship with them, and some manufacturers sell them as stand-alone units, sometimes targeted at professionals (EIZO), sometimes just as a high-end home monitor (Dell). If you are professionally working with photography, you just cannot come around having one. The downside is that it shows sRGB material way oversaturated, and almost everything you encounter on the Web is in sRGB.
For further information, you may like to read the Wikipedia articles on exposure, HDR and colour spaces, they are pretty good IIRC.
Edit: Additional explanation because of your comment
To clarify things: HDR in itself has nothing to do with files. You can have HDR photography with film without ever creating a digital representation of your image. What you are describing in your comment is just one way to store the information about a HDR image using a digital technology.
My first sentence was quite poorly worded. Still, what I meant by it holds: monitors cannot represent big exposure differences, so there are no HDR monitors. To represent the big difference in exposure present in a HDR image, lighter and darker shades are used in lieu of getting the monitor to emit more or less light per pixel, but this conversion happens in the software which does the digital developing, not in the monitor. Using a monitor with a wide gamut would give you a better representation of the way the original looks, as long as your software doesn't downconvert the information somewhere on the way. Depending on what you understand under "LDR space", you can see this as a way to avoid the lossy mapping from 12-bit (or more) of image sensor data to a 8-bit colour space, or only as a better way of doing the inavoidable mapping. In any case, the result looks nearer to the origninal.
The answer posted above is not completely accurate. HDR images have little to do with the sRGB color space. They are about contrast ranges. Most monitors do not have that much contrast range, they can only display a black that is so black/grey while at the same time displaying a white that has X-amount of brightness. The brighter you drive the display the greyer the blacks become.
Color spaces come into this because there are many steps between bright white and the deepest black. A larger color space displaying monitor can display a brighter range, but when delivered that range still has to be mapped to the 8-bits of image for each color. If the monitor has a wider gamut than standard than its blue may be bluer or green greener. Mapping into that space means at maximum green the monitor may display more green than standard. This means the image you see is different than what the photographer captured. The image is supposed to have a green different than the one you're mapping to.
There are some prototypes,and a few low-volume commercially available HDR displays. These work by using a grid of LEDs as the backlight to an otherwise traditional LCD panel. This allows the display to have a much wider dynamic range than a traditional LCD display with a uniform backlight.
A regular LCD display can handle between 2 to 3 stops of dynamic range. The HDR displays push this to around 5 stops. Even so, they can't yet come close to the human visual system, which can deal with about 14 stops (a "stop" is essentially a doubling of the amount of light emitted).
The technology was introduced by Brightside, and was acquired by Dolby Laboratories. A Google search for dolby hdr will reveal a fair amount of info.