You can do that kind of thing with the calligraphic brushes that come with AI. You'll want a tablet to get that kind of control.
Drag any of the Artistic_Calligraphic brushes to the regular brush palette, double-click it, set the diameter to vary based on pressure and move the slider over so that you get a big range.
If you don't have a tablet, you can sort of fake it using some of the selections in the Artistic_Ink library with prefabricated heads and tails.