Maybe you noticed that, unlike previous non-"S"-year iPhone updates, the iPhone 7 and 7 Plus look a lot like their predecessors. In fact, a few small details aside (such as the speaker grille and antenna design), they're almost identical.
The technical specifications on Apple's website for the iPhone 6S and the iPhone 7 (including all the Plus models), suggest they have they exact same dimensions. The buttons are all in the same place, and despite the lack of a 3.5mm jack for analog headphones, your old case should, theoretically, fit the new model. The location of the headphone jack has been replaced with a speaker grille which shouldn't interfere the fit of a case.
However, there is one major design difference that matters: the camera.
The lens protrusion on the iPhone 6 and iPhone 6S is small and juts out from the casing, almost as if it's glued on. With the iPhone 7, the camera optics are much larger and the casing slightly curves up to the rim of the camera housing. With the iPhone 7 Plus you have a dual-camera layout, which is not just taller than the old optics, it's several times wider, as well.
The official Apple cases for the iPhone 6S look similar to those for the iPhone 7, but they will not fit properly. This means if you spent $99 on the Smart Battery Case, you'll have to buy a new one for the latest iPhone.
This change will affect other accessories as well, such as the Olloclip.
Fortunately, everything else should work just fine, including your wired headphones via an included Lightning adapter.
reading•Planning on using an old case with the iPhone 7? Nope.
Nov 18•Apple Park opens its doors to outsiders
Nov 17•iPhone X is one of Time's 25 best inventions of 2017 (Apple Byte Extra Crunchy, Ep. 110)
Nov 17•Apple Park's visitor center is now open for business
Nov 17•iPhone X vs. 8 Plus vs. 8: Choose the best iPhone for you