The blood oxygenation level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal is a widely-accepted marker of brain activity. The acquisition parameters (APs) of fMRI aim at maximizing the signals related to neuronal activity while minimizing unrelated signal fluctuations. Currently, a diverse set of APs is used to acquire BOLD fMRI data. Here we demonstrate that some fMRI responses are alarmingly inconsistent across APs, ranging from positive to negative, or disappearing entirely, under identical stimulus conditions. These discrepancies, resulting from non-BOLD effects masquerading as BOLD signals, have remained largely unnoticed because studies rarely employ more than one set of APs. We identified and characterized non-BOLD responses in several brain areas, including posterior cingulate cortex and precuneus, as well as AP-dependence of both the signal time courses and of seed-based functional networks, noticing that AP manipulation can inform about the origin of the measured signals.