Let's give it a try:
First, a comment for each album
Hybrid Theory: where it all started, it's either HT or Meteora. No other option for me.
Meteora. It's another masterpiece
MTM: I love the balance between soft songs and not-so-soft songs. Few skip songs. In Pieces being of the best for me
ATS: Waiting for the end is one of the best LP songs, but I don't like many songs that much (robot boy, BITS, blackout, WAK) and so many interludes
Living Things: Not a fan of the album, but some songs I love. But many (many) songs to skip (STB, LGM, Victimized, UIB). But I love LITE, IMR and Powerless, and have a soft spot for I'll be gone
THP: I love many of the songs in the album, but I think some songs are just mid (UIG, GATS, War, Rebellion). But FM, ALITS, and Wasteland are really really good
One More Light: I don't know if I like it more or less that LT, but it has many mid songs, but the only one I don't like it's Heavy. Sharp Edges and Nobody Can Save Me are one of my favorites.
FZ: It should be up soon (5th at least), I really like the album and with some time could be very high in my list. For now, besides TEM i don't have a song that gets me like the other albums, but it will. So far is a no skip album (which for me it's really rare)
Now the rank:
(1-2 very interchangeable)
1. HT
2. Meteora
3. MTM
(4-5-6 depending on the mood)
4. ATS
5. THP
6. FZ
7. OML
8. LT
I think FZ could be 5th or even 4th, but doing a ranking is really hard, because some albums have masterpieces but the album itself is not that great, and that happens me with THP for example.