MAME can place multiple objects on the screen in arbitrary positions using the layout feature. Of course, this won't help with any other emulators.
Here's an example .lay to move a 4x3 (horizontal) or 3x4 (vertical) game screen to the left or right on a 16x9 monitor:
<mamelayout version="2">
<element name="widescreen">
<rect>
<bounds x="0" y="0" width="192" height="108" />
<color red="0" green="0" blue="0" />
</rect>
</element>
<view name="HLeft">
<backdrop element="widescreen">
<bounds left="0" top="0" right="192" bottom="108" />
</backdrop>
<screen index="0">
<bounds left="0" top="0" right="128" bottom="108" />
</screen>
</view>
<view name="VLeft">
<backdrop element="widescreen">
<bounds left="0" top="0" right="192" bottom="108" />
</backdrop>
<screen index="0">
<bounds left="0" top="0" right="81" bottom="108" />
</screen>
</view>
<view name="HRight">
<backdrop element="widescreen">
<bounds left="0" top="0" right="192" bottom="108" />
</backdrop>
<screen index="0">
<bounds left="64" top="0" right="192" bottom="108" />
</screen>
</view>
<view name="VRight">
<backdrop element="widescreen">
<bounds left="0" top="0" right="192" bottom="108" />
</backdrop>
<screen index="0">
<bounds left="111" top="0" right="192" bottom="108" />
</screen>
</view>
</mamelayout>
192x108 is specified as the backdrop dimension instead of 16x9 so it's easier to divide by 4 and 3. The rest of the numbers come from placing a 1.333 aspect picture on the 16x9 screen.
Regarding other emulators, it's much easier to force a position when you're working with a window instead of fullscreen. When you're in fullscreen mode, the program believes that it is responsible for presenting everything to you, including the black background. In windowed mode, you can use a utility like AutoHotkey to push windows to where you want them.
As for what to do with the spare area, special moves for fighting games comes to mind. Or pretty much anything that others are using 2 monitors for. In the example layout above, the backdrop could just as easily have been a .png image, so its use is only limited by resolution and imagination.
--Nexusmtz