This can be a complex answer, and quite often, the outcome is that it depends what you print on, meaning you might need to change it or recalibrate often.
On White Point
White point from the perspective of the human eye is a very subjective thing, as the eye automatically "recalibrates" itself to differing white points depending on the kind of light that dominates a scene. To start the discussion, lets start in the middle: Sunlight has a white-point of about 5500k (although it tends to range in reality from between 5000k and 6000k). As you noted, most screens these days are calibrated by default to a white point of 6500k, which appears to be more white than lower values. Some screens often come with a built-in range of settings, such as 5000k, 5500k, 6500k, and some even as high as 7500k and 9300k or around there (which have a bluish tinge to them.)
Why Set a White Point?
The key reason why we set a white point is not so that it appears "white" to our eyes. The main reason we set a white point is to match the "white" on screen to the "white" of the material and environment in which your photos will be viewed. There is no single correct, standard viewing environment, and depending on how you normally publish your images, the white-point you select may be different than other photographers. A couple of the most common viewing mediums are on a computer screen (i.e. you publish your work to Flickr, 1x.com, etc.) and print.
White Point for Screen Display
If you really don't care much about print, and only really exhibit your work online, you might want to stick with a white point of 6500k. That is a very common white point, and the default for many computer screens, particularly lower-end ones. The color profile sRGB, a standard and very widely used color gamut, is also aligned to a 6500k white point. Most images saved for viewing on a computer screen should be saved using the sRGB color profile when possible (using a wider gamut, such as Adobe RGB, may be necessary if your image has very vibrant colors, particularly greens, but also reds and violets, as sRGB is a more limited white point. Adobe RGB also uses a 6500k white point.) Using 6500k will mean that what you see with your calibrated display will generally be very similar to what your viewers see when they browse your work online. There is no guarantee of this, of course, as screen vary in minute to major ways for a very wide variety of reasons, but it is a reasonable baseline.
White Point for Prints
Things get more complicated when you involve print. Papers tend to have warmer white points much of the time, so the common default of 6500k makes white on a computer screen look quite a bit whiter than it does on print. Papers also come in an extremely wide variety, from very very warm (4800k or sometimes even warmer), to very bright, almost blue white (7500k or cooler.) This is where screen calibration is really important, as having your screen matched as closely to the papers you print on will make it easier to generate properly calibrated and color balanced prints.
When it comes to paper, the story is extremely complex. Paper is a very old enterprise that extends back over 600 years. There are some general buckets that you can put papers into, however: fine art paper, canvas, and coated/brightened. For me, and for many photographers, there is nothing quite like a good fine art paper. These papers come in a huge variety, from many material sources, including the common wood, but also uncommon sources like cotton, bamboo, and sometimes even mixed blends that may include animal fibers. The tones and textures of fine art papers are amazing, and can have a huge impact on the appearance and appeal of a final print. Fine art papers tend to be warmer, and its best to calibrate your display to a white point of 5000k. Canvas is another type of printable paper these days. There are also a variety of canvas papers, however much less variety than fine art papers. Canvas is also a warmer type of media, and can range from 5000k to 5500k. The third major bucket of paper includes coated papers. Many fine art papers are uncoated, non-brightened, letting the natural fibers produce the tone and texture of the paper. Coated papers cover the natural fiber base with one or more coatings to provide a smoother surface, surfaces that are more receptive and ideal for ink jet printing (or other types of printing), and protected from the elements allowing a longer-lasting print. Coated papers often also include optical brighteners to make the white point of the paper brighter and "whiter". Such papers often have much higher white points than natural papers, up to as high as 7500k or so. A white point of 7500k is extremely bright, bordering on blueish. Papers with optical brighteners are sometimes difficult to calibrate for, as the brighteners often depend on the type of light they are viewed with. Many brighteners use UV reactive components, and produce their brilliant white by reflecting UV rays from natural sunlight (or artificial gas lighting like flourescent tubes.) As such, their white point can change depending on the lighting.
Choosing a White Point
So, what should your white point be when you calibrate your display? It depends, and it may change frequently if you publish to a variety of media types. I myself use the DataColor Spyder3 system to calibrate all of my hardware. I normally calibrate to a white point of 5000k, for a few reasons. First, most of my work I print on my Canon 9500 II, on fine art papers. I am a big fan of Hahnemuhle, Moab, and a few others. All of the papers I use, such as Photo Rag and Canvas, have warmer 5000k white points. I also publish a lot of my work online, and every so often I recalibrate to 6500k to preview my images online and see how they look. (With the Spyder3 Pro, it is very easy and very quick to change white point and do a short recalibration that takes about 5 minutes.)
Another reason to use 5000k as your base white point is if you use Photoshop. Adobe Photoshop has its own color management system, and internally by default it is calibrated to a white point of 5000k (often abbreviated D50, along with D55/5500k, D65/6500k, etc.) By calibrating your display to 5000k, you sync your hardware to Adobe Photoshop's default settings, which makes it a little easier to convert and/or apply color profiles and see accurate results.
Finally, the light you view your prints under has a direct effect on what "white" looks like. If viewing prints in sunlight, they will generally be lit by "normal" white light, at a temperature of around 5500k. Artificial lighting can vary. Common light bulbs range in temperature from about 2500k to 4200k, which is quite warm. Flourescent lighting, which is less common in homes, is hard to nail down. Often cooler, 6500k to 7200k or so, they also output greener or violet lighting. Sometimes they come in warmer variants that are more similar to standard bulbs. Calibrating to a warmer white point helps balance out differences between what you see on screen, and what you see in print.
More to the Story
The calibration story does not stop at white point. If you really want to have accurate color calibration throughout your entire workflow, there are additional factors, such as luminance (how bright your screen is), gamma, environment lighting, etc. If you have additional questions about calibration, feel free to ask other questions, and I'll see if I can provide a useful answer.