I became a 7-string addict when I bought mine. Now my Les Paul feels incomplete. It has a big fat 50s neck but it feels tiny in my hands when I'm used to spanish guitars and 7 strings. I was really lucky to find a 7-string what wasn't your usual robot-machine-methulll-über-shreddy-whammy-superstrat, but something more "me" (read: les paul-like). I can live with the flaws in blanace and playability to have that "real-tone"(got Mules in it even. I wouldn't be surprised if they are the only set of 7-legged Mules), but if I can ever afford a custom guitar, I'm getting a 7-string LPDC. I haven't ever seen that either, heh.
To me, the 7th string is very usuable. A simple thing like extending a barre chord with a low 5th can add a lot to the expression of the chord. Then there's the big fat B -> D# chords that are suddenly possible.
For soloing, I also prefer 7-stringed guitars over drop tunings. The notes are still "where they are suposed to be" if you know what I mean, so it's as easy to improvise as on a standard tuned 6-string. And you can do bigger sweeps and runs without having to move as much horisontally, aswell as wider intervalic string skipping licks. Yes, right now it sounds like I'm just describing wankage but when you're used to the technical advntages, the creative aspect comes easier.
8-strings though I have no experince with, but I'm a big Meshuggah fan so I'll probably end up giving in someday and buying one. Those Blackmachines look incredible, though not my style.