Overhead racks
Every row has racks above the seats. They fit carry on bags and small suitcases, roughly up to 160 cm in total.
Behind the last row
On the Tokaido, Sanyo and Kyushu lines, the space behind the last row of each car is the oversized baggage area. You get it by reserving a seat in that last row.
On other lines the same space is also the most practical spot for big bags, so a last row seat is always a good choice.
With a Japan Rail Pass, seats with an oversized baggage area are included at no extra cost. Book them by scanning the QR code on your pass at a Shinkansen ticket machine or at any staffed JR desk. Get your Japan Rail Pass
Baggage compartments
Some newer trains have reservable lockable compartments near the doors. They appear as an option when you book if your train has them.
At your feet
There is good legroom, so a small suitcase can stay in front of you. Window seats in rows of two (D and E on most trains) have a bit more room.