Going to take these in an arbitrary order:
BackgroundWorker (#5)
I like to use BackgroundWorker when I’m doing things with a UI. The advantage that it has is having the progress and completion events fire on the UI thread which means you don’t get nasty exceptions when you try to change UI elements. It also has a nice built-in way of reporting progress. One disadvantage that this mode has is that if you have blocking calls (like web requests) in your work, you’ll have a thread sitting around doing nothing while the work is happening. This is probably not a problem if you only think you’ll have a handful of them though.
IAsyncResult/Begin/End (APM, #4)
This is a widespread and powerful but difficult model to use. Error handling is troublesome since you need to re-catch exceptions on the End call, and uncaught exceptions won’t necessarily make it back to any relevant pieces of code that can handle it. This has the danger of permanently hanging requests in ASP.NET or just having errors mysteriously disappear in other applications. You also have to be vigilant about the CompletedSynchronously property. If you don’t track and report this properly, the program can hang and leak resources. The flip side of this is that if you’re running inside the context of another APM, you have to make sure that any async methods you call also report this value. That means doing another APM call or using a Task and casting it to an IAsyncResult to get at its CompletedSynchronously property.
There’s also a lot of overhead in the signatures: You have to support an arbitrary object to pass through, make your own IAsyncResult implementation if you’re writing an async method that supports polling and wait handles (even if you’re only using the callback). By the way, you should only be using callback here. When you use the wait handle or poll IsCompleted, you’re wasting a thread while the operation is pending.
Event-based Asynchronous Pattern (EAP)
One that was not on your list but I’ll mention for the sake of completeness. It’s a little bit friendlier than the APM. There are events instead of callbacks and there’s less junk hanging onto the method signatures. Error handling is a little easier since it’s saved and available in the callback rather than re-thrown. CompletedSynchronously is also not part of the API.
Tasks (#1)
Tasks are another friendly async API. Error handling is straightforward: the exception is always there for inspection on the callback and nobody cares about CompletedSynchronously. You can do dependencies and it’s a great way to handle execution of multiple async tasks. You can even wrap APM or EAP (one type you missed) async methods in them. Another good thing about using tasks is your code doesn’t care how the operation is implemented. It may block on a thread or be totally asynchronous but the consuming code doesn’t care about this. You can also mix APM and EAP operations easily with Tasks.
Parallel.For methods (#3)
These are additional helpers on top of Tasks. They can do some of the work to create tasks for you and make your code more readable, if your async tasks are suited to run in a loop.
ThreadPool.QueueUserWorkItem (#2)
This is a low-level utility that’s actually used by ASP.NET for all requests. It doesn’t have any built-in error handling like tasks so you have to catch everything and pipe it back up to your app if you want to know about it. It’s suitable for CPU-intensive work but you don’t want to put any blocking calls on it, such as a synchronous web request. That’s because as long as it runs, it’s using up a thread.
async / await Keywords
New in .NET 4.5, these keywords let you write async code without explicit callbacks. You can await on a Task and any code below it will wait for that async operation to complete, without consuming a thread.