There are a few threads of recommendations, so if you have a search around the first few pages of this subforum you'll find some suggestions. Also, all the bands that have individual threads here are popular.
What sort of stuff are you into? Heavy, not so heavy, jazzy, acoustic, pop...? :?
Anyway, some bands/artists that I recommend if you're new to j-rock are *takes deep breath*:
Dir en grey (hard to classify, not metal really, I guess you'd call them hard rock or something of that kind, but their music is really diverse, so it's worth giving a quite a few songs of theirs a listen. Songs of theirs that I like are Jealous, Fukai, Machiavellism, Cage, Hydra, Drain Away, Dead Tree and Pink Killer. If you prefer ballady-type things, listen to Ain't Afraid to Die).
Malice Mizer (gothic with classical influences. Again, they've produced some songs which are heavy-ish - Beast of Blood - and others which sound almost classical - anything off the Bara no Seidou album!)
MUCC (rock with fantastic basslines. Quite simply this band is great!)
Kagrra, (you must definitely listen to Kagrra, they are so good! Unique sound, you can hear the influences from 'traditional' Japanese music. Again, really great basslines... and guitar... and drumming... and vocals... hehe).
Psycho le Cemu (pop-ish, dance-ish music, very catchy; they have ballads and heavier stuff too).
Gackt (the archetypal Japanese pop-rock singer/musician! Actually he used to be singer with Malice Mizer, but now like
the most famous Japanese pop star! He's a good musician who knows how to write a catchy chorus...)
L'arc en ciel (pop-rock).
Galneryus (sort of metalish rock with excellent guitar playing).
Lucifer Luscious Violenoue (one of very few female j-rockers, but worth listening to because of the music regardless of gender. Non-heavy gothic ballad thingys).
Kozi (I laugh at myself because I'm a Kozi fanatic, but I'm serious in my recommendation! Kozi's music is really varied, which is why I'm suggesting it. Some is goth - Katarushisu/Catharsis album - some is classical - Izayoi no Tsuki album - and some is just plain weird!... think fairground music meets ska...
)
SID (excellent, excellent vocals. Not heavy music, but not exactly pop... I don't know how to classify them but they're really good).
The Zolge (really good punk-rock band, now sadly disbanded though).
Other bands/artists I love include Gazette, Deathgaze, KuRt, Kagerou, Miyavi, X Japan (of course! wow! topic!), GISM, Aushvitz, Kra, Scissor, 12012............. and... too many to mention... you get the picture!
EDIT: The stuff that I've mentioned is music both that I happen to like and that is popular among 'j-rock fans'. But that doesn't mean it's the most popular in Japan - like you say "the Japanese equivalent of Bob Dylan". I've never had the chance to visit Japan, so I can't tell you what is popular over there, but I know from my Japanese ex that the bands such as I like aren't the ones that are mainstream in Japan (apart from Gackt and L'arc en ciel...). To find that out you really need some advice from someone who lives there...
Hope this is helpful and good luck on your search!