In Civ I, reloading was a way of life for me. Of course, that was when (at least in the Mac version) it was the gateway to a cheat. For whatever reason, it wouldn't remember which of your units had moved during the turn of your save. So, all you had to do was save at the end of your turn, quit, reload, and boom, all your units had their full movement again. It was the original infinite movement! Of course, your cities never got to produce anything, but it was a small price to pay.
In Civ III, I found myself reloading less and less. In the beginning, I was still possessed of the Final Fantasy mentality (i.e. I can't miss anything, I want all the Magicite/Materia/Summons, etc., so whenever I miss one, I'll reload from an earlier save.) However, once I began to get more in the strategy/tactics mode, this fell away, simply because if you miss it in this game, you can get it in the next, and there's no one item that you HAVE to have in order to win or have a complete experience.
On the whole, I think I agree with most people here. Competition, it's flat wrong. One-on-AI, while you're learning, it's a useful tool to see how to fix certain mistakes or how things would play out if you did it differently. However, if you want to master that level, and not make those mistakes to begin with or learn how to recover from them, you can't reload.