In Spinelli's paper, I believe their front end, as a differential high pass filter, has a lower cut off at 0.033Hz. It works well for ECG applications. Though you may want to change it according to your application. For example, For EMG I prefer to follow SENIAM or ISEK standard to avoid movement artifacts.
Which signal are you interested in? If it is ECG (band of interest 10-50Hz) you should put it a little bit higher (e.g. at least 0.5Hz as Sampath mentioned) because you can get a respiration-induced artifact. This artifact can go from 0.1Hz (6 respiration per minute) to 0.5 (30 rpm).
One of the most critical measures in the ECG is the ST segment, often a flat line between the end of the QRS and beginning of the T wave. Such changes indicate significant ischemia or even an ongoing infarction. Changes are often seen as a DC shift (elevation or depression), hence a very low frequency change which the instrumentation must be able to measure. The lowest heart rate one might see is 30 beats/min or .5 Hz. Recognizing that the phase response of a filter is at 50% of its maximum at the corner frequency and that phase shifts would have the most significant impact on the ST segment, it has been the standard to use one decade lower for the ECG high pass corner frequency, or .05 Hz.
thank you, ECG is clear, but what about with frequencies as EEG or any other... Is there any algorithm or system to designt the cutoff frequency or is always already 0.5?