If I understand you correctly, you want a list of Foo objects which have different types of Outputs, right? Since these outputs are of different types, you would have to use casts here anyway.
However, the following idea might help. How about you declare a non-generic interface called IFoo: ¹
public interface IFoo
{
    object Output { get; }
}
and then implement it in your abstract class:
abstract class Foo<T> : IFoo
{
    abstract T Output { get; }
    object IFoo.Output { get { return Output; } }
}
Then you can declare a list of IFoos:
class Bar
{
    List<IFoo> Foos;
}
When accessing those foos, you can either retrieve the output as an object via the interface:
var myObject = Foos[0].Output;     // type ‘object’
or you can try to discover the real type if you know that it can only be one of a few specific types:
if (Foos[0] is Foo<string>)
    var myString = ((Foo<string>) Foos[0]).Output;   // type ‘string’
You can even do filtering based on the type, for example:
// Type ‘IEnumerable<string>’ (rather than ‘IEnumerable<object>’)!
var stringFoos = Foos.OfType<Foo<string>>().Select(f => f.Output);
¹ You can also make this an abstract base class called Foo and have Foo<T> derive from it. In that case, you would need to mark Foo<T>.Output with the new keyword and use base.Output to access the abstract base member.