Many of the first proof-of-concept fMRI experiments were block designs with two conditions. In a block design, each condition is presented continuously for a period usually longer than 20 seconds. In the earliest fMRI studies (see Kwong, 1992, and Ogawa 1992), one commmon paradigm was to alternate between 60 second blocks of a flickering visual stimulus, and blocks without stimulation. Analysis was done using a simple t-test between values of the MR signal collected in the "on" condition versus the "off" condition. In addition to comparing "on" versus "off" conditions, block designs have been used to look at differences between more similar conditions as well. (Kanwisher has used block paradigms where the subject is presented with blocks of pictures of faces and blocks of pictures of houses to probe high-level features of the visual system)
These block designs tend to be quite powerful for assessing BOLD signal magnitude differences between conditions. The length of the blocks of stimulation allows for the HRF to reach maximal values, while the inter-stimulus intervals are long enough for the HRF to return completely to baseline during non-stimulation. The downside of block designs is that they are not powerful at estimating the shape of the haemodynamic response (aside from its magnitude).
Block designs are also not as useful with many experimental paradigms having special requirements. In the DM paradigm for example, subjects are scanned while they are presented with single words. After scanning, they are given a list of words composed of words seen earlier mixed with new words, and instructed to mark them as "old" or "new". For the old words, the fMRI trials are analyzed according to whether or not the subject remembered them during the second part of the experiment. In this example, blocks of "remembered" and "forgotten" trials cannot be reliably constructed, because the event categorization depends on a parameter outside the control of the experimenter.