It's Back to the Future! Arguably one of the greatest films of all time(s), certainly one of the greatest scripts: funny, tightly plotted, memorable characters, intelligent, great for all the family and has an excellent guitar solo. What more do you need? How about the answer to just how many trips does the DeLorean make through time in the series? The answer is ten but for a more detailed explanation of those trips see the graphic above.
Most of the time-travelling is done in Part 2, which also features Biff getting hold of the car and popping back to 1955, as shown by the lines under the timeline. I've also zoomed in on the frantic 10 days in 1955 where most of the action centres around. This diagram also shows the two key lightening strikes (the first that sends Doc all the way to 1885 in Part 2 and the key plot device from Part 1 that gets Marty back to 1985). As a bonus, I checked and it took Marty one minute 22 seconds to from 0-88mph for his first time travel.
I've deliberately simplified the timeline as much as possible to exist on one plane (apart from the alternate reality as highlighted by the Doc in Part 2) but if you're going to be really precise about how the timelines would work, read up on this very comprehensive post on the Back to the Future wiki (there's actually eight of them...).