Maximum Game Resolution
Does your game depend on a resolution? If not you could try to create your game around a minimum resolution and work up.
It's a very open ended question. I never usually try to approach a game design with a resolution in mind
A number of different things affect your end resolution. Take a game like titanfall for insurance. 1080p on ps4 and 720p on xbox one. But that's the high end.
At the end of the day. You can tweak things as you go. Don't let res dictate your aspirations at the start.
I think resolution is truly only a limiter when it is targeted at mobile games, but of the inherent nature of smaller screen with similar resolutions.
1280x720 is a very common size.
8K UHD are nowhere near consumers yet, but will be in a few years. That's 7680 x 4320.
The general approach is to decide the aspect ratios you will support and scale everything else using appropriate tools. In 3D that means setting your view matrix so it takes up the whole world and textures are resized automatically through texture mapping routines. For 2D that means upscaling or downscaling as needed and possibly adding black bars above/below or to the sides, depending on which way the resolution relates to the ratio you built for.
Even cell phones are starting to get 2560x1440 screens now. You should make a game that works with a *minimum* resolution *and anything higher*. Also make sure you can support refresh rates higher than 60Hz (144Hz monitors are getting popular for PC gamers). Also make sure you support different aspect ratios (4:3, 16:9, 16:10, 5:4, etc).
You can ask the user's video device what resolutions and refresh rates they support, and let the user pick from that list.
In addition to resolution, there are different physical monitor sizes. You might have a cell phone with a 2560x1440 screen that's only 5 inches diagonal, or a PC monitor that's 1920x1080 with a 28 inch diagonal. Games often have a "UI Scale" setting which scales elements up or down in case the defaults don't look good on a particular screen.
If your game has a "HUD" or some other kind of screen where you arrange 2D elements around the edges of the screen, you should position them relative to the corners or centers of the screen rather than a specific pixel amount (which changes per resolution), but size them taking aspect ratio into account (or else squares and circles will become rectangles and ellipses).
I personally run 7680x1440 with triple 2560x1440 27 inch monitors. There really shouldn't be a cap for your max res. If the users system can handle it then why not let them.
The graphics hardware certainly isn't lagging behind these resolutions. 4K with high/ultra settings with 40-60fps being achievable. There have been 8K tests as well with Nvidia Pascal TitanXs achieving medium settings with playable frame rates so were not too far behind. Next graphics generation should yield 8K viability.
Moral of the story is scale your game to fit a wide variety of resolutions. Nothing is more infuriating then running something other than native monitor resolution.
Given the resolutions the OP mentioned, I think she's asking what an appropriate minimum resolution is these days, not a maximum.
Or rather, she's asking what's the maximum acceptable minimum resolution for a game is (i.e. she wants it high to avoid hassle of handling very low resolutions, but not so high that it loses significant numbers of users).
The best bet is to look at the stats collected by Steam and Unity and make a decision based on that: http://hwstats.unity3d.com/pc/display.html / http://store.steampowered.com/hwsurvey/
800x600 would get you almost everybody. The problem with 1024×768 is that a lot of people also have 1280x720, so maybe 1024x720 would be an appropriate pair of minimums (not that it's a res that anyone really has).
I think resolution is truly only a limiter when it is targeted at mobile games, but of the inherent nature of smaller screen with similar resolutions.
1280x720 is a very common size.
Or for VR in the early days (e.g. Oculus DK1)