I would not expect much.
Emulation on the PC it eeking its way forwards but PS1 and earlier is still the main focus for most things (give or take the handhelds but they are seldom that much more powerful) and I doubt much the PS4 brings to the table will change things there.
At the same time I don't see it being powerful enough that it is going to be a way to bring a lot more to the table. ROM sizes relative to download options, bandwidth and storage available are also considerable impositions for a lot of those (everything that is not an optical disc likely fits on a "round or two in the pub costs more" priced USB flash drive/SD card these days, start going into DVD and beyond world...) which further troubles potential popularity.
Many of the later consoles are also somewhat lacking in games as well (Nintendo's post SNES and post DS efforts were game deserts a lot of the time, even if the consoles themselves sold well enough that some consider them a success) and can also have aged like milk on the graphics front, which emulation can only do so much to address.
Today everybody has a laptop, tablet, phone or raspberry pi to shove into their TV (if they even care to use a TV rather than hold a phone close enough that it takes up the same amount of their visual space, plus is their own private thing). To that end all the little nice applications that were only possible or 100x more viable when TVs and computers did not have matching inputs (or resolutions) by default are pointless.
Equally most of the games are on PC as well and I don't see any kind of ROM hack making or cheat having cutting a big swathe through them, even more so if mods=ban and people somehow think paid online is not only acceptable but desirable (and even then "want more variety/tighter gameplay in multiplayer" is 70% of the reason for modding things). Minor exception if the online dies or it is viable to have a "for homebrew" device for the masses, though prices probably won't get there too soon (360 and to a slightly lesser extent PS3 prices cratered at one point, wii even more so after the wii sports crowd flogged them to go onto the next fad, but I am not seeing that for the PS4 too terribly soon).
I should also note that while I can debug things without them if I don't have an emulator, especially on modern games, it is a pain in the arse to do much more than token efforts where "might as well be a new game" is a weekend project on something like the GBA or DS where I have great emulation. Being a modern device someone might care to hack me some nice OS level game savestates, memory viewer, cheat search, breakpoints/watchpoints/logging, disassembly, macros and whatnot and dump it all over network (or have SSH/telnet going in) such that I can fake it well enough.
Basically I doubt we will ever see another xbox, GBA, DS, PSP or Wii, and if we do it will be because the hardware is so damn cheap (or cheap for the power) it just makes sense to not use an old PC/pi/tablet, because everything else folds inwards and goes locked down (some tell me android is heading there -- trying to find something I can root, replace the battery by removing a cover, shove a SD card in, have a headphone jack and have HDMI out is actually easier said than done), because the hardware affords the option to do something that nothing else can (that is also desirable -- give me a perfect setup for emulating some old arcade stuff that is an arse ache to do any other way and I will be interested, as will the 1000 people on a handful of sites but nobody else will likely care).