Depends on how you're looking at it, really. Like Jackie Silver mentioned, there are some who argue that since roughly every area of the galaxy has been travelled through, it's all done. However, if you look at the visited system maps that we do have, you'll notice that much has only been zipped through by a few Commanders, and there are large volumes of space entirely unexplored. Or, as I like to say: plenty of places left in the galaxy where you could hide the entire human bubble. In my opinion, saying that the galaxy has been explored is like driving a car through a dozen cities without actually stopping in them, and then saying that you've been to the entire country.
Of course, the galactic core has so many systems that it's never going to be fully explored. But when it would come to hand-placed stuff, it would be evil of FD to put anything in just a wholly random place there. (So, Raxxla?)
But yeah, if you're looking at cartographic records, or being the first to go to some region, since we're years after release, you're mostly out of luck. Of course, since this is an MMO game, the moment that our FSDs receive any kind of new improvement, within days everything new that can be reached will be reached.
If you're exploring to find things inside systems, you are and will always be good to go.
Hm, now I wonder how it would look if EDSM drew a map of only the systems that have at least a dozen bodies scanned.
Oh, and as for hand-placed stuff, what has been hinted at by FD but yet to be found: the original "bubble" of the Guardians (although that might be in the locked Regor sector) and two megaships from the Dynasty expedition. The problem with the latter is that the search area is far too wide, so it would require an enormous community effort to find something which is tied to a storyline that's already done. (Would have been nice if the Zurara left behind actual beacons and stuff to find though, and then the system name wouldn't have needed to be literally spelt out to be found.)
Oh, and supposedly the Thargoids were / are present in someplace else than the Pleiades, but were never found. (Then Frontier decided they want them found ASAP, and turned on the encounters there too. Basically shoving it under our noses.) Given the way that the aliens can currently be found though, you'd have to look much closer than people generally do when they are travelling. Which would take a lot more time.