Q:

Can autothrottle be used without autopilot (and vice versa)?

In commercial passenger aircraft:  
Can autothrust be used with A/P disabled ?
And can A/P be used without using autothrust?
Citable references very welcome!
If the question depends on a specific aircraft type, then please B777.

A:

They can be used individually, yes. When flight directors (or autopilot) are on then they dictate what auto throttle should do. But it's not a good idea to fly manually, use auto throttle and have flight directors still on and here is why:

When autopilot is off but the flight directors are on and auto throttle is on you can select a vertical mode like flight level change or vnav and then auto throttle will take commands from that selected vertical mode. In flight level change, for example, thrust is either full climb thrust or idle thrust, which means: If you as a pilot flying don't pitch for speed then you just have throttle stuck in either full or idle and you either overspeed or stall. Not a good idea to leave flight directors on and use autothrottle on its own!
When autopilot is on but auto throttle is off then autopilot and you select a vertical mode like vnav or flight level change then you are in command of delivering thrust, so you need to advance throttle to start climbing or you need to retard throttle to descent. And if you use vertical speed mode you are in control of airspeed. So you have to monitor your climbs and descends and airspeed but it's not too bad. In the end there are other aircraft types that have an autopilot but no auto throttle.
When autopilot is not engaged and flight directors are off then auto throttle controls just speed, this is safe. Airbus' landing checklist has an item for this: "auto thrust? - SPEED".

This applies to 777, 747, 737, A320, A380 and probably (have not checked the fcoms) A350, A330, A340, 757, 767

A:

Yes it can. Autothrottle on most large aircraft (including 777) is considered a separate system from autopilot. To that end, the modules/boxes that control the autothrottle and autopilot are separate as well. This adds a bit of redundancy in that losing autopilot doesn’t mean you also lose autothrottle and vice versa.
Edit: I couldn’t find a clear system data reference to show how the integration of the two systems can be split and/or combined. As was pointed out in the comments, there are multiple sources of information showing this is possible. One such example is this excellent depiction of the FBW (fly-by-wire) systems on the 777. In there, the language alludes to the concept of the autopilot and autothrottle being able to be independently engaged, emphasis mine:

Disarming the Autothrottles through the AT disarm switches on the Mode Control Panel (MCP) will prevent them from "waking-up" at low airspeeds. In such a case the Autopilot, if engaged, will give up on maintaining level altitude and let the aircraft descend in an attempt not to exceed a given angle of attack. An aural and visual warning will alert the pilots of this.

