I rarely actually delete my browser history, but by default, my browser (Opera) only stores a certain amount of sites visited, anyway. So, in practice, only relatively recent history is actually still available.
I find it occasionally useful. Sometimes I accidentally close the browser, and then it's handy for getting back to where I was (especially if I'd followed a lot of links). And sometimes I want to look up more about something a day or two later. Being able to search the history is often fairly efficient then.
I don't use bookmarks much anymore. I used to, but that lead to the problem of having so many bookmarks that they weren't helpful anymore. Nowadays, I use Firefox's Bookmark Bar for the most important links at work, and when I want to save something for future reference at home, I usually save it to my hard drive. But even that is fairly rare.