I love Wunderlist, but...
 

it only allows you to create one layer of child tasks. I need to be able to create a never-ending layer of child tasks.

Are there any similar apps/services that allow never-ending child layers? There are so many Project Management apps out there, I'm sure several of them do what I want, it's simply so hard to track down and test them all.

It would also be nice if you can assign dates to the child tasks, you cannot in Wunderlist, only the parent tasks.

For OS X or Windows?

Would prefer web-based so it's easily accessible from multiple devices.

Omnifocus has both features you're looking for, but it isn't web-based(there's no web interface).
There's an OS X, iPhone and iPad app and everything is synced through their own syncing backend.

Are you using the GTD method or do you have your own system?

I have tried a few different systems, but I always find that I start bending the way I really want to do things, just to fit into somebody else's system. I don't have a concrete system, just a little method that works for me.

I used to use Wunderlist but now I just use Evernote for pretty much everything.

Taskpaper - pretty clean and minimalistic, you can throw some styling though ... it gives you the abstraction, so the rest depends on you - e.g. how to organise your stuff, how deep to be your nested lists and etc.

You can check also Workflowy, which is web based ... it's model is more like creating a mind map (have you tried mind maps?), but with notes; e.g. it has the different layers and child tasks.

But, both are not very user friendly on mobile, IMO ;)