Wait, you mean there are other explosive movements besides cleans? :(
edit - because i didn't think my first answer out very well -
I think the poster above me said something very keen - squats are huge in this department. I saw huge improvements in explosiveness and speed when I focused more heavily on the big three, especially squats and deads. Since we're talking sports, I'll say that as a wrestler, focus on my squats allowed me to stay in better stance and shoot more powerfully, and deads helped me finish shots strong. So sometimes the best way to develop explosiveness is in heavy core work - get your legs and back, which are basically where explosiveness is gonna come from anyway, to be accustomed to very heavy loads lifted at a certain tempo, and you'll find that bearing your own bodyweight is much easier for you.