A lot. Resolutions as hard coded settings are a thing of the past, a huge number of modern games populate their resolution list from the graphics card drivers which collate a list of all supported resolutions from your monitor.
How many games are built with 4k in mind so that HUDs scale appropriately and art assets fit correctly? Not that many. I recently noticed when playing JazzPunk that in 4k HUD elements when wanting to be hidden are simply moved slightly outside of what would presumably be a 2560x1600 screen size. Playing Anno 1404 recently the cutscenes which add upper and lower bars to give a faux cinematic feel during cutscenes don't span all the way across a 4k screen which looks daft.
But fundamentally, minor issues aside, most games and game engines support 4k or really any arbitrary resolution, so the rendering is just fine, it tends to be things like the HUD, text and other 2D overlays which tend to have issues aligning.