If you want to limit or control the amount of power gaming
1. find new players; or
2. establish the limits based on the setting first and enforce them
I am not not sure which edition your playing. If 3e and wiling to do some "work", you can start with:
1. No Free multiclassing. Multiclassing requires training (see the DMG variant on training). This requires finding a trainer, convincing them to train you, and having the time to train. How long do you think it takes to train to become a monk, a wizard, to learn proficiency in every armor and martial weapon? You the GM decide and the character must sit out that long. If the PCs are travelling in some remote area, then they may be, completely, out of luck.
If the trainer is another PC or NPC travelling with the party, you might even set feat and skill pre-reqisites to represent acquiring skills as one goes through "apprenticeship"
2. Prestige Classes: determine which (if any) are appropriate for and exist in your setting. Tie them to specific cultures or organizations. Again, players cannot simply take them. They have to know about them, gain entry into organization, convince them to train the character, etc. "Knowing" about a PrC might mean growing up in the appropriate culture while others need to spend time in the culture. Other times, the organization might be secret and not easily known and have to be discovered in play.
And, again, if PCs are in the wrong area of the world, they are out of luck.
Now, there may be some instances where the character might be able to be a member of the "organization" whether an academy, temple, guild, culture, etc. at first level. In such a case, you might require them to start as a class variant to represent their specific training (see the PHB Customizing a character, the DMG, and UA class variants). This may eliminate some or all of the need to multiclass. The class variant might have the armor and weapon proficiencies and the skill list of the the PrC, maybe a variant of a standard class feature (e.g., detect undead instead of detect evil) or more limited spell list. However, they still need to meet the pre-requisites of the PrC to level in it. This brings me to the the following question:
3. Why are they multiclassing? Is it to meet a reasonable (for the given campaign setting) fantasy archetype or background not supported from the start by existing classes, but by jumping hoops or penalizing them in other ways (e.g., cross class skills). A rogue with wilderness skills or martial capability, a bard that is a lore keeper/historian for a barbarianclan/tribe in which wilderness skills are more appropriate, a divine bard that is a priest for a particular deity, a rage based warrior that grew up brawling in back alleys and pubs of a city rather than a wilderness based tribe/clan.
a. Consider using Unearthed Arcana style class variants and/or some additional base classes. Sometimes multiclassing is done to meet a concept that is a common fantasy archetype not supported without jumping hoops or penalizing the character in other ways.
Myself, I like to use the OA Shaman (replaces the monk in my campaigns), Green Ronin's Psychic's Handbook, Shaman's Handbook, and Witch's Handbook.
I also make use of UA class variants like the Barbarian Hunter (with favored environment and cultural weapon groups), several bard variants, martial rogue, and wilderness rogue
b. Consider using the Urban/Wilderness skill swap from the Cityscape web enhancement.
c. Boost the skill points per level for the cleric, fighter, and sorcerer and, maybe, add a few extra class skills.
5. If the players are trying to take levels to gain several armor and weapon proficiencies and/or boost good saves and avoid taking the appropriate feats, limit a classes initial armor and weapon proficiencies to starting characters. After first level, the only way to gain new armor and weapon proficiencies is by taking the appropriate feats either through leveling or bonus class feats. Similarly, require characters to use the save progression of their initial class. After first level, they can improve it by taking the appropriate feat(s) to represent new training.
6. Are they multiclassing, because spellcasters dominate? Tone down the spellcasting classes. Some places to start:
a. Clerics: Create you campaign's deities and set their spell lists to what is appropriate by their domains (see Tailored spell lists in the 3e DMG). If necessary, you might want to rewrite some of the domain spell lists by swapping certain spells for others. This cuts back on the versatility of the class making them more thematic. It might even remove some core spells from the game if they don't fit any of the deities.
Limit Planar Allies to a specific creature associated to an individual deity. Build each deity an ally for each version of the spell. This is what shows when the spell is cast. For example, if the deity's associated creature is a an eagle, start with that as the base form. Increase the size, add templates, etc. to scale its power.
You might even want to look at spontaneous divine casting from UA which reduces the number of spells known. Myself, when I ran 3e, I used spontaneous divine casting with a cleric's spells known limited to their deity's domains plus a handful of spells that I felt were appropriate for all characters.
b. Wizards: require them to find their spells as per the variant in the DMG. The spells they can learn must come from this list. For specialist wizards, you might tailor their spell lists (again, see the DMG variant on tailoring spell lists).
c. Druids: You can drop them for the Green Ronin Shaman, ban or add more pre-requisites to Natural Spell, place more limits on the form that can be Wild Shaped into and/or the creatures that can be companions (by fiat, the terrain in which the druid grew up and/or or controlling what creatures are in your setting, etc.), and limit which PrCs are available.
d. limit the spells from alternate source to what is appropriate for your campaign.
So many years ago I started playing D&D. It was great. I joined a group in college; none of us really knew the rules but we had fun. We made decisions on the spot about rules. We didn't care if our choices were optimized. No matter what happened, we did our best to not say "No" when "Yes, but it will be difficult" would do. We just played and had fun.
But time marches on and the old group has graduated and gone their separate ways. I've found other groups and for the most part they've been good. But with each new group I've been with, the rules have taken more precedence. Character and role-playing have taken a back seat to power. And now I find myself saying "No" more and more often; becoming afraid that some of my players are cobbling together some sort of multi-class monster that I won't see coming until its too late.
And so I sit here now, staring at my campaign notes, wishing that there was some way for me to recapture the games of old. When I wouldn't have to sit at the table and listen to the GM and two players argue about the physics behind a falling book for a half hour. When no one cared what your classes were, so long as you were having fun.
Maybe I'm just nostalgia blind. But I'm curious what advice you have to give me enworld. What can I do?