The Archmage is not as bad as some others. An Archmage does give up something (spell slots) for his High Arcana; many WotC PrCs give up little to nothing at all. It's also a very different kind of PrC, meant to be taken at the upper levels, and was probably the basis for FFG's Legendary Classes.
To answer the original question, sure, if you find a good PrC you like, run it by your DM and get his OK. PrCs are pretty popular in general, and many players like them. Some classes have a much better selection than others, and some classes give up much more to get a PrC than others do. But even clearly overpowered ones like the Hospitaler or the Doomguide (from Faiths and Pantheons), that give up very little and gain a lot, probably aren't going to break the game.
The potentially dangerous part comes when you add bits and pieces from all these different expansions and d20 books, each giving a boost in power. But that's not too hard to keep under control if your DM knows how to say No.