Reason for Inter-stimulus-Interval in psychology studies
If you've ever tried doing an experiment with no inter-stimulus interval (ISI), you know from first-hand experience that it makes a difference in several ways:


If the task is about reaction times, you don't really have time to prepare. I.e. there is an attention-based interference effect. For Flanker tasks, Stroop tasks, go-nogo tasks, etc., you want to measure the optimal performance and hence you add ISI to reduce the interference. In other tasks, you set a short ISI exactly because of the interference effect, e.g. in some conditions of Conner's Continuous Performance Test, on Vigilance tasks to keep challenging attention (see e.g.McCormack, 1958), etc. Low ISIs are also quite useful for Task-Induced Stress.
There are other carry-over effects than a reduced/biased attention. For example, repetition priming is substantially reduced for longer ISI's (e.g., Ferrand, 1996). If you are not studying repetition priming, such effects constitute noise or a confounder, so you want to reduce it by having reasonable ISIs.
With ISI=0, the next stimulus appears to be caused by your response, so it feels like your key stroke "belongs" to the new stimulus rather than the previous. This can be confusing.