I think the most flexible box is the Roku which does a ton of services. But it doesn't appear to do the BBC iPlayer and it doesn't go Vudu.

Vudu is the most restrictive in terms of devices since it only appears to work on game consoles like the Xbox 360 and PS3, various TV's (in the US of course) and similarly BluRay players (again US models only) and some devices.

The D-Link DSM-310 does Vudu but not Amazon. So I think it's hard to get by with one box except the PS3 (and possibly the Xbox 360) which does Netflix, Vudu, Amazon and Hulu+.

As an aside I have never been able to get Netflix working on my Roku using UnblockUS and TCL's transparent proxy. I know it does work since when I tried out a VPN it worked fine.  It must be using port 80 for some of its communication to to the Netflix servers which is getting trapped while the other devices like the PS3, GoogleTV, Android/IOS tablets/phones don't appear to use port 80 at all.