This is really tough. But before I go into any list I think it is important to set the ground rules for the ranking, for example the OP didn't include Ghosts because it is an instrumental album.
So, I guess my first criteria would be that only NIN official releases count and that this is not a TR list. So no GWTDT, TSN or HDA. The second, is that this is purely subjective based on my tastes right now, with maybe some consideration given to the effect these albums have had on me over the years. I will not, however, be giving any consideration at all to the public's perception of the albums. So TDS being one of the hallmark 90s releases won't have any effect on my ranking it but the fact that TF was my first ever NIN album may solidify its position at number 1 because I'm a sentimental motherfucker and it was basically my first love.
I know exactly what 1 and 2 will be, and I know what is going to be last, but 3-8 are really tough choices.
1. The Fragile - Trent's most masterful work. Two CD sprawling opus that changed the way I listened to music. From the first time I heard it, NIN were my favorite band. If I was a little older and had been introduced to TDS first, then TDS might take top spot, but even ignoring the sentimentality of The Fragile, it still takes top spot. This has been and always will be my favorite NIN album. The day that the Ultra Deluxe Remastered Edition is released is the day my life will be complete. Goddamn, I really hope that it is still in the plans at some point.
2. The Downward Spiral - Easy number 2 choice. I don't feel like a whole ton more has to be said because these top two seem fairly obvious to me - and apparently almost everyone else because TDS and TF are numbers 1/2 on almost every list.
3. Hesitation Marks - This might be the euphoria of a new album dropping but I'm pretty confident in this choice at number 3. HM feels like TR has taken all of my favorite things from WT, YZ and The Slip and combined that with a new direction and HM is what came out.
4. Ghosts I-IV - When I was in University I bet I listened to this album 200 times because any time I was writing a paper, I would put it on repeat and it would be my sountrack to writing for hours on end. I disagree with the comments in this thread that it is too long, isn't as tight as it could be, is directionless or anything else that has been mentioned in this thread (although I might use some of those comments for a GWTDT review but I digress). It is just so beautiful in so many ways. Never has an album that is without a single word said so much to me.
5. With Teeth - Again my sentimentality is probably what puts this ahead of my 6th-8th choices, as this was the first NIN album that I heard on release day (at the time anyway). It certainly has some weaker songs, like The Collector, but to this day Sunspots is in my top 3 NIN songs of all time.
6. Year Zero - It does have a couple of tracks I'm not overly fond of but I love the way it represented such a shift from WT and then to The Slip. Both WT and the Slip seem to be more on the Broken side of the pendulum, being more rock oriented with a raw stripped down kind of a feel. YZ feels now like very much a precursor to HM in that it was very electronic focused.
7. Broken - I couldn't decide where the heck to put this. Slight disadvantage in that it is so short but it is also the album I'd most likely describe as being like getting hit with a sledge hammer. What it lacks in length, it certainly makes up for in intensity.
8. The Slip - I really wanted to put this higher but there is just so many strong candidates in the previous 7 spaces. Even in an all-star game, someone still has to get picked last, or in this case second last. Good album and unlike some of the previous choices there isn't a single song I don't like but it also doesn't have any game breakers that take it to the next level.
9. Pretty Hate Machine - As mentioned, only my 1/2 choices and this one were set in stone before I even thought about ranking the albums. I don't dislike PHM, and I'm definitely too young to have appreciated its effect in the late 80s/early 90s, but even though it has grown on me, it still sounds a bit dated and is the only album I don't listen to regularly. I also prefer the live versions of pretty much every song that is played live. There are a few songs in the NIN catalogue that I prefer live but rare that I prefer all the live versions to the studio versions. I don't hate it. I just don't love it as much as the others.
If I were to incorporate TSN and TGWTDT, I'd put TSN in 4th and bump Ghosts down to 5th and so on. And then I'd put TGWTDT somewhere around Broken/The Slip, maybe ahead of both or between or behind both. Not sure. That one never grabbed me like the others. Still is hard to place too because while I like that record, it is really the last half of the album that I love, specifically AATCHB. Overall though I'd have to place it in the lower half. Probably same or similar to TGWTDT.