1) It’s dead simple. Write down the spells you prepare, cross them off as you use them. You get X number per day. Couldn’t get much simpler than that.
2) It forces players to think ahead and try to anticipate the challenges to come. Sure, there will be some all-purpose spells that will be prepared almost everytime, but no matter which system you use there will be spells of greater utility than others and those spells will see greater use.
3) Naturally, players can’t anticipate everything they’ll encounter. Preparing spells in advance encourages players to find inventive uses for the spells they have prepared. I know some DM’s don’t like this. They think casting a Light spell into the eyes of an Ogre to blind it is a cheese move. Later editions of The Game have increasingly tightened up their spell descriptions specifically to reign in this kind of gameplay. However, I think inventive spell use is part of what makes D&D fun (for me, at least)…even when players easily take out my master villian casting a spell in a completely unexpected way.
4) It’s mechanically modular (like most of D&D), so it’s easy to twink if you don’t like it. You can tinker around the edges a bit, or rip its guts out and replace it entirely with a system more to your liking, and doing so will (usually) have little mechanical effect on the game’s other systems.
A note on spell memorization: some have pointed out that it doesn’t make sense that a caster should ‘forget’ a learned spell after casting it. But I think it depends on how you look at things. For one, it’s magic, not the laws of thermodynamics, so it can’t really be explained in any rational sense. But that’s also a bit of a cop-out argument, so here’s another way to look at it: preparing a spell is more like refreshing your memory, like studying for a big exam. After the test, how much information do you really retain? For most people the answer is, not much. Yet another way to look at it: if memorizing reams of information is so easy, why do lawyers keep law libraries in their offices? Why do doctors need medical references? Professionals have to reference information in their fields all the time, and not just to learn about the latest advances. So, likewise, a wizard needs to reference his/her spell books and ‘bone up’ on the material they think they’ll need for the coming day’s adventure.
All that said, I don’t think the Vancian system is perfect. For one, the power curve could be flattened out a bit. Low level casters could use a few more spells starting out, at the expense of some higher level spells later on. I also think the system would be a bit more intuitive if spell levels directly matched caster levels, so that a 2nd level caster casts 2nd level spells at character level 2 instead of character level 3.
Finally, please don’t take this as a polemic against alternative spell systems. I’ve played a wide variety of alternative systems and most of them have been fine. I just seemed to me that, of late, the Vancian system hasn’t been getting its due credit.