As a DM, I really prefer to only allow a limited number of prestige classes, if any. I view PrC's as a way to add flavor to a campaign for specific things such as say an order of Knights or a secretive order of arcane casters, etc. Otherwise, I firmly believe that the base classes in the PHB are more than enough variety for the players.
In the previous campaign, I allowed pretty much any and all PrC's and things got way out of control. In many cases, the PrCs that got taken were broken super-classes. As a result, everyone jumped on the PrC-bandwagon and was either in 1 or more PrC's or working their way into one when that campaign ended. As a direct result of the abuses I observed, the following (current) campaign had some strict guidelines on how Prestige Classes would be allowed into the campaign. There were a lot of upset players at first, partly because I had banned much of the material from books like Sword & Fist, Tome & Blood, etc that they had purchesed. However, after some time, they've gotten used to it and can see that there were a lot of problems in the old campaign directly caused by problems with the PrCs that were in use.
Unfortunately, I still get hounded from time to time about adding more PrCs into the current campaign, so I realize there is still an issue there. Players seem to think that each of their characters should have an option to choose from multiple prestige classes, and not having enough cool ones available to pick from is somehow hurting their gameplay. :\ They also seem to think that any PrC printed by WotC such as those in the DMG or the new Complete Warrior should be allowed without question. I'm currently allowing about half of the PrCs from those along with another half-dozen or so that I've created from scratch just for this campaign. The reason I'm not including all is partly due to balance with other classes and part of its due to flavor. It's just hard to convince them of that.
I agree that with multiclassing a lot of the features that many PrC's offer can be reached. Rather than PrC's, I'd much rather see characters tailor themselves with their feats. I strongly believe more feats should be available, especially ones that provide the abilities currently unique to some PrCs. If done correctly, it would fix the problems with balance as well as allow for better custom tailoring of characters without requiring the need for PrCs.
