With the case of something like a Wacom tablet, it merely takes a bit of time to get used to it.
I always recommend new drawing tablet users put their existing mouse, trackball, or trackpad in a drawer for a couple weeks and only use the stylus for everything.
It will be difficult at first and feel unnatural. However, the more you use it the more accustomed to it you get and eventually it'll be more comfortable than a mouse or any other input device.
Once you are comfortable with the tablet itself, it's merely a matter of configuring brushes/tools in whatever app you prefer to match your traditional drawing style. I find, for me, the Blob Brush in Adobe Illustrator more closely mimics anything I do on paper than any other brush in any other application. So, if I'm free-handing something, I immediately jump to the Blob Brush with predefined settings.
In the end, it just takes practice to improve the hand-eye coordination since you are actually drawing one place and looking in another place.
There's also some difference in tablet models. For example the Bamboo tablets have half the pressure sensitivity of any Intuos tablet, and one fourth the pressure sensitivity of the Intuos 5 line. Any pressure support is better than none. But the additional levels of support in the better tablets allow the apps to pick up more subtle nuances while drawing. Not to mention the fact that the Intuos tablets support additional features such as tilt and rotation to grab as much natural hand movement as possible.
If you've got an Intuos tablet, you may want to consider the Art Pen stylus for it. The added input data from that stylus can help a great deal. I much, much, prefer the Art Pen over any of the other styluses (?? Stylii ??).
Of course, there's always the Cintiq line of surfaces. These allow you to draw and look in the same location more closely mimicking traditional paper. But the price tag isn't anywhere near the same as the top of the line Intuos.