You got me curious about this myself, so I did a quick inventory. Most of my papers are fiber, 9.5x12, unless otherwise indicated. And, with a few exceptions, I've got multiple boxes of each.
Primarily for lith printing:
Fomatone 131, 132, 532(II), the old 542 (5x7), 333 (4x6)
Foma Variant IV 123
(all Foma papers pre-reformuation)
Fotospeed Lith (8X10)
Forte Polywarmtone
Slavich Unibrom 160
Primarily for contact sheets, proofs, and postcard exchange:
Fujibro WP FM3, KM2, KM3, FM, AM (all RC, from 4x6 to 8x10). Fuji papers are obviously my cheapest option in Japan, which for some reason is not necessarily true of their film.
Fuji Rembrant V (not for proofing, just a small box to experiment with for final, fiber-based prints). But I think I'll stick with Ilford.
And for exhibiting prints that are non-lith:
Ilford MGFB Warmtone
Ilford MG Art 300
Ilford MGIV RC pearl (for proofs or postcards)
I loved the Foma papers for everything, but since the reformulation have decided to use them only for lith prints now. Even though I've been printing for years, that's a bit of a misnomer, since I usually only get into the darkroom for 2 or 3 sessions a year (those sessions may last from a couple of days to a couple of weeks). So I'm still trying to master what I've got and settle on a select few papers for specific processes/looks. I'm hoping with my move to Kyoto in the near future that I'll be able to find a place where I can have a dedicated darkroom that I can work in on a regular basis and make a dent in quite a number of the boxes I have.