I'd like to third the thoughts of Crothian and Magic Rub.
My players can choose any class combination (read core and Prestige) that they wish so long as mechanically the classes fit. In other words, no paladin barbarians unless they undergo an alignment change. So far, none of my players have taken more than 1 PrC anyway simply because they are not the powergaming type. However, they do have that as an option.
I adhere to the principle of gaming should be fun and if the player will have fun taking multiple PrC's, so be it. With that said, the class selection must make sense. For example, taking a level of gladiator is going to require some connection to gladitorial combat and arenas. This could mean something as simple as meeting a fellow gladiator who showed the character the basics or something as extensive as becoming a slave and being forced into the arena for several months. I definitely prefer my players to let me know what they plan on doing ahead of time so that I can work whatever character progression they want into the story, but I am pretty much completely open to whatever that character progression may be.
I figure that the game mechanics exist as a guideline and a system of rules. But when you immerse yourself into your characters or NPCs you would not think that oh my female friend wielding the rapier and lightly armored is a Fighter8, Duelist6. You would think of her as my female friend who wields a rapier and is lightly armored. You might call her a duelist, but would not associate that with class progression. An even better example is Aramek from Solid Snake's story hour. I am a player in his game and I know from having played with the NPC from the beginning that he has levels of fighter, barbarian, ranger and some other things. But I don't think of the dwarf as a barabarian/ranger/fighter/etc. I think of him as Aramek - a badass dwarf wearing the skin of black dragon I helped him kill and wielding a shield and warhammer. To me its not about the class selection but the character.
I would even be open to such smackdown concepts as Super AC man, Super Save man, etc. I figure that with most of these smacks, they have extraordinary power on one note but must give up some things on the other. And even if they don't, it will simply mean that they are the best of the best and to challenge them I will have to have equally maxed out opponents.
For example, take the smacked out fang of lloth sneak attacker. Sure its great to get the 12 total attacks (with haste, expert tactician, 3 main attacks, bite, 5 off hand attacks, and 1 extra attack from improved two weapon fighting) and you can definitely lay waste to someone with this tactic. But after the surprise round and your enemy goes down his friends are all around you. With your +14 BAB at 20th level, mediocre AC, and lack of surprise (now they all have their dex bonuses) you are toast. Not to mention you look like a freaking spider. Do you really think that you are going to be able to go anywhere but a devout lloth worshiping city. Definitely not. Are you going to be able to associate with many NPC's - certainly not.
Certain multiclass combos flat out will not work. For example, the singh rager and the iaijutsu master combo that has been posted simply would not work because it requires you to be both a lion and a crane (clans in Rokugan). This is impossible and you therefore have to choose one or the other. Sure you can be a member of one clan and then defect to the other. But do you really think that other clan is going to give you access to learning their most powerful secrets when you have shown how dishonorable you are in the first place. I think not.
Finally, while I allow every official D&D product (therefore PrC) as well as all AEG stuff and all SSS stuff, I clearly distinguish between worlds. Someone who wants to multiclass the summoner from SSS' Relics and Rituals and the divine emessary from FRCS, can. However, doing so is going to require knowledge of both worlds in the form of skill points, will require knowledge of the specific classes, again, through skill points and roleplaying, require extradimensional travel, require appropriate languages (to learn all that information), require access to all that information - either through the Library of Alexandria(located on a secret demiplane in my multiverse/multiplane/multidimensional game) or specifically traveling to those worlds. In other words, that will be no easy task and will probably wind up being the focus of the entire character concept - simply to acquire that info.
btw - the library of Alexandria is one of the best guarded secrets in my multiverse and is the hardest demiplane to access.