What kind of camera do I need to capture deep space images?

Unfortunately, a lot of images like the one you show here are digitally altered and it is difficult to get comparable results. The image above shows the Milky Way, looking approximately at its center, which appears to us to be in the constellation of Sagittarius.

To get such a detailed view of the comparatively dark nebulous structures, however, you need to use really long exposure times. Unfortunately, because of the stars' apparent rotation, exposures above approximately 25 seconds (for wide angle lenses; the smaller your lens angle, the shorter the time) begin to show star trails. So I doubt that the image you show was really created as one exposure. If so, the photographer must have used an extremely low-noise semsor with exceptionally high sensitivity.

The linked "star trail" image (which shows the telescope I work for, by the way) used a technique called "stacking". To create it, 70 1-minute-exposures were added together. This is a common method that allows you to get very good images using a normal DSLR and an external timer/trigger.

If you stack the images so that the star "pinpoints" are on top of each other, you will get a detailed skyscape with blurred foreground. This is what I suppose was done in your example image: The sky was images with a series of exposures, stacked together for greater sensitivity, and the foreground has likely been added afterwards.

Of course, instead of doing that much digital manipulation, you can also follow the traditional route and mount your (D)SLR on a tracking mount. A good description with sample images that show what to expect from real-world exposures is given on the "bedfordnights" Geocities page (link to archived copy at Internet Archive).

Edit: I forgot to address your question regarding location. Yes, it depends on the location: For one thing, the center of the milky way (which is its brightest area) gets higher above the horizon when you move from the poles to the equator. But most importantly, images of the quality you show above are only possible from the darkest locations on the planet (which sounds exotic and adventurous, but essentially means "anywhere where there are no human settlements causing light pollution in about 200 km radius").