It should be noted that two factors limit the amount of space available to me under the seats: 1) I have the automatic clutch version of the FJR, and some of the main seat's storage is taken up by this system; and 2) I have my seat in its lowest (of two) positions. Despite this I have been able to fit all of the things that I consider to be must have accessories. It did take a little creative Tetrising...
Manuals. I have a Ziplock freezer bag with my bike's manual and warranty, plus the manuals for my on-bike gadgets (like my Cardo Scala Rider O2 communications pod).
Tire Repair/Maintenance. Under the manuals are a CyclePump air compressor and a cordura zip case with the contents of a comprehensive tire repair kit (based on the 'sticky strings' variety). Do not plug the CyclePump into the 12V accessory socket in the front storage compartment! That circuit only has a 3A fuse and will blow instantly. Instead, I use the Battery Tender lead coming off the battery (with appropriate fuse, of course).
Tools. I replaced the placeholder tools provided by Yamaha's Department of Humorous Gags with a complete set from Cruz Tools, the Metric M3. This roll-up had to be flat-folded into thirds in order to fit under the passenger seat.
Miscellaneous. In the front storage compartment, I keep the bike registration and insurance papers in a Ziplock. I also have a set of Rok Straps in a small Ziplock. Finally, there are five sets of foam ear plugs in a small Ziplock and the pod to my Cardo Scala Rider O2.
Here are some additional pics of the details: