It has repeatedly been reported in the medical literature that the EEG signals of Alzheimer's disease (AD) patients are less synchronous than in age-matched control patients. This phenomenon, however, does at present not allow to reliably predict AD at an early stage, so-called mild cognitive impairment (MCI), due to the large variability among patients. In recent years, many novel techniques to quantify EEG synchrony have been developed; some of them are believed to be more sensitive to abnormalities in EEG synchrony than traditional measures such as the cross-correlation coefficient. In this paper, a wide variety of synchrony measures is investigated in the context of AD detection, including the cross-correlation coefficient, the mean-square and phase coherence function, Granger causality, the recently proposed corr-entropy coefficient and two novel extensions, phase synchrony indices derived from the Hilbert transform and time-frequency maps, information-theoretic divergence measures in time domain and time-frequency domain, state space based measures (in particular, non-linear interdependence measures and the S-estimator), and at last, the recently proposed stochastic-event synchrony measures. For the data set at hand, only two synchrony measures are able to convincingly distinguish MCI patients from age-matched control patients (p < 0.005), i.e., Granger causality (in particular, full-frequency directed transfer function) and stochastic event synchrony (in particular, the fraction of non-coincident activity). Combining those two measures with additional features may eventually yield a reliable diagnostic tool for MCI and AD.