Well, it seems that what happened to Square is this:
Square took a big risk with the Final Fantasy movie. It didn't pan out. They eventually "merged" with Enix to save themselves. This merger was actually highly unequal; Enix became the ruling entity (in Japan, the Dragon Quest franchise rivals the Final Fantasy franchise, and some might say it wins). The Square franchises probably will stay around, as Enix flexes their new muscles, but they may seem different. The Enix franchises will definitely stay around, and I'm expecting good things from DQVIII (I'm one of the few North Americans who prefers Dragon Quest to Final Fantasy).
As for other companies, Monolith is made of pretty much the same team that made CT, CC, and Xenogears. Lets just hope they get the rights to the Chrono series, and that they don't go bankrupt from the Xenosaga series (an epic series is a huge risk; each game can be expected to sell less than its predecessors). Nautilus, the branch of Midway responsible for Shadow Hearts, has picked up a very dedicated (if small) following. If they stick around, they could easily grow to overtake Square franchises (if not Enix franchises).