Any acid that yields a concentration of hydrogen ions with a molarity greater than 1 will be calculated to have a negative pH. For example, the pH of 12M HCl is calculated to be -log(12) = -1.08. However, you can't just dip a glass pH electrode in the HCl and measure a negative pH. Glass pH electrodes suffer from a defect called 'acid error' which causes them to measure a higher pH than the real pH. It is very difficult to apply a correction for this defect to obtain the true pH value.
Also, strong acids do not fully dissociate at high concentrations. In the case of HCl, some of the hydrogen would remain bound to the chlorine, so in this respect the true pH would be higher than the pH you would calculate from acid molarity.
To further complicate the situation, the activity or effective concentration of hydrogen ions in a concentrated strong acid is higher than the actual concentration. This is because there is so little water per acid unit. While pH commonly is calculated as -log [H+] (negative of the logarithm of the hydrogen ion molarity), it would be more accurate to write pH = - log aH+ (negative pf the logarithm of the hydrogen ion activity). This effect of the enhanced hydrogen ion activity is very strong, and makes the pH much lower than you'd expect from the acid molarity.
So... you can't accurately measure extremely low pH with a glass pH electrode and it is difficult to tell whether the pH is lowered by the increased hydrogen ion activity more than it is raised by incomplete dissociation. Negative pH is possible, but not something you can show.