Hydroastatic acid, HAt, would, if it existed in measurable quantities, be one of the strongest simple monoprotic acids in existence, and the strongest of the hydrogen halides. This is due to astatine's low electronegativity, which in turn stems from the large distance between the nucleus and the 5 electrons in the 6p orbitals. Consequently, in solution, it would disassociate readily and completely with its proton.
It would also undoubtedly be extremely hazardous, due not only to its acidity, but also to astatine's radioactivity. However, since the earth's crust generally contains no more than 30 g of astatine at a time, and it has only been synthesized in microgram quantities, it is unlikely that one should ever encounter such a substance.
Thanks to vuo for correcting the scope of my writeup; as he pointed out, the initial version neglected to mention diprotic acids and superacids, which can be much stronger.