How should I deal with object hierarchies in a RESTful API?

There’s no reason not to combine these.

• api.example.com/user/{user_id} – return a user representation
• api.example.com/channel/{channel_id} – return a channel representation
• api.example.com/user/{user_id}/channels – return a list of channel representations
• api.example.com/user/{user_id}/channel_list – return a list of channel ids (or links to their full representations, using the above links)

When in doubt, think about how you would display the data to a human user without “API” concerns: a user wants both index pages ({user_id}/channel_list) and full views ({user_id}/channels).

Once you have that, just support JSON instead of (or in addition to) HTML as the representation format, and you have REST.