I see a lot of people in blog posts and here on SO either avoiding or advising against the usage of the Thread
class in recent versions of C# (and I mean of course
To answer the question of "are there any cases when it's necessary or useful to use a plain old Thread object", I'd say a plain old Thread is useful (but not necessary) when you have a long running process that you won't ever interact with from a different thread.
For example, if you're writing an application that subscribes to receive messages from some sort of message queue and you're application is going to do more than just process those messages then it would be useful to use a Thread because the thread will be self-contained (i.e. you aren't waiting on it to get done), and it isn't short-lived. Using the ThreadPool class is more for queuing up a bunch of short-lived work items and allowing the ThreadPool class manage efficiently processing each one as a new Thread is available. Tasks can be used where you would use Thread directly, but in the above scenario I don't think they would buy you much. They help you interact with the thread more easily (which the above scenario doesn't need) and they help determine how many Threads actually should be used for the given set of tasks based on the number of processors you have (which isn't what you want, so you'd tell the Task your thing is LongRunning in which case in the current 4.0 implementation it would simply create a separate non-pooled Thread).