I'd think the real question you want to ask is not "Should I have multiple save slots" but "Should players be allowed to make multiple saves of their game/save wherever they want?". It feels to me like you are wondering if you want to prevent players from making multiple saves to try different approches/paths and choose the one that worked out best, to stop them from save-scumming and/or that you would want your game to be a little more deterministic/hardcore. It could be a viable option, although it might please a different public. In any event, I don't think limiting the number of save slots is the way to go. It just prevents different people from playing the game at the same time, or a player keeping his old finished (or not) game files to try a new approach/path. Here are 3 options you might want to consider for your issue, though. Note that each of them makes your game that little bit more hardcore and might discourage more casual players. It's not inherently a bad thing, just something to consider.
1) Should players be allowed to duplicate their saves? The traditional way of saving is it opens a screen with all the save slots and you save however you like. Maybe you don't want this, though. Maybe, when starting a new game, a player chooses in which slot he wants his game to be saved, and whenever he saves the game afterwards it automatically saves in that slot (and that slot only) without opening the save slots screen and the whole shebang. Players couldn't fork their game in this manner, couldn't go back as easily to change paths, it would be a little more deterministic/hardcore. A single game would go a single path, and if you want to try other stuff, you have to start a new one. Although, as some else said, keeping duplicate files to avoid save-games boing corrupted for whatever reason and permanently lost would be something to consider.
2) How/When/Where should players be allowed to save? In more modern games, you can typically save (almost) wherever you want, at any moment you want. It's pretty flexible, but maybe you don't want that, maybe you think it breaks the atmosphere or screws up your game's balance somehow. Older RPGs had specifically identified save points. You could skip it if you pleased, go back to save as many times as you wished, etc., but at least you couldn't save anywhere. It limits the player a bit on how/when he forks his game. Maybe you won't save scum that boss so much if you have to go through two thirds of the dungeon each time you aren't pleased with the outcome of the fight, as opposed to saving right before the boss (or worse, during the battle). There is yet an even more hardcore option: have a few pre-select auto-save points. The player doesn't really control where and when the game saves at all. Maybe it saves when you complete or start a dungeon, enter a town or any other pattern you like. Save scumming and forking might become nigh impossible, the game will become that much more deterministic. This last method might be more appropriate for episodic games / games divided in short chapters, but who's stopping you from using it anywhere else? It could work.
3) Should you consider using perma-death? Okay, this is not directly save-related, but it's the kind of thing you think about when you hear of single-save-slot-games. It gives off a rogue-like vibe, hence perma-death. Of course, this is a pretty peculiar mechanic and should be considered carefully before being chosen. Generally, games are tailored around it, and it really speaks to a particular public, which might not be your target audience. This generally goes better with single save-slot games because those games imply relatively short playthroughs. Having multiple saves is much less significant if your average playthrough lasts about half an hour. Of course, to avoid repetition and becoming too boring too quickly, such games rely on heavy randomization, which is another challenge and peculiar game feature.
So anyway, just a few things to think about. Hope it helps //rmwforums.s3.amazonaws.com/emoticons/default_smile.gif
