About 95% of the people I see in gyms use the 'pyramid' system where they're adding weight to each set of the same exercise. They'll start with X number of reps and the number of reps will decline on each set as the weight increases.
Honestly I think most people do this because they don't know any other way, and look to see what others are doing and just follow suit.
The science behind that system, as I understand it and as it was explained to me, is to exhaust the slow twitch fibers early so that the body will recruit fast twitch fibers on subsequent sets. I don't necessarily think this is right or wrong, just a very popular method.
I personally always start with my heaviest working set (not talking about warm-ups here) and drop weight on each subsequent set. The logic is that I want maximum energy and intensity going into my heaviest set which should already be recruiting fast twitch fibers based on weight, speed of reps and intensity. Also, with reducing weight on each set, I can stay within a target rep range (let's say i'm trying to hit failure within 4-6 reps for instance). With the pyramid system, if you started with for example 10 reps and increased weight on subsequent sets, you're obviously going to do fewer and fewer reps. By the time you get to your (last) heaviest set (arguably the most important working set), you're most likely already fatigued and cannot put maximum intensity and effort into the set. To me it seems like short changing yourself.
IMO reducing weight after each set just makes more sense. I'd like to hear what you all do, and why? Give me the science behind it.