Some classes have dive count prerequisites (although nobody ever asked to look at my log to prove I was there). Some charter operators want to see your log, although the only ones I've run into were in Australia. But mostly, the log is for you . . . it can help you remember how much weight you used with a given combination of exposure protection and tank; it can help you remember things you wanted to note about how to dive a given site. Log entries can bring back great memories, too -- I love the page in my log book when I passed GUE Fundamentals. I drew fireworks all over the page!
Of course, many of us eventually just end up downloading our computers, and keeping a lot that way -- but I still make narrative notes in that log, and I still record weight or anything notable about the dive.