The same question was asked when bitcoin was new. We now know the answer to that. The same can be said about altcoins. But not all alt-coins will have the same future as bitcoin. If it is just a copy paste of bitcoins code, then it will be trash. If it does not offer something new or any added value, it will be trash. But if it has a unique characteristic that can be valuable, then I say that coin have a future.
Everything that has started has its own future. 
So, I guess Altcoins will have its own future because it's value is continuously upgrading. Base also on what I've read, this coin have a future because of its own characteristics.