His weakest solo album is Vol. 2. But that album's full of some of his most popular songs ("Hard Knock Life", "Can I Get A...", "Money Ain't a Thang", "Money, Cash, Hoes"), and two of his best songs period - "A Week Ago" and "Reservoir Dogs", so you may want to peep it. If you don't want to hear the whole thing, just grab "A Week Ago" and "Reservoir Dogs" and you're straight. "Nigga What, Nigga Who" is also dope.
Reasonable Doubt and The Blueprint are considered his best albums, so just go ahead and listen to them through.
In My Lifetime, Vol. 1 is his most schizophrenic album - some straight-up pandering to popular tastes, and then some good old shit. "Imaginary Player" is one of his best songs, as is "You Must Love Me." "Where I'm From" is a pretty tough track (and a source of hilarity in Fade to Black, if you've seen that). "Friend or Foe '98" and "Streets Is Watching" are also quite dope, as is "A Million and One Questions" (also peep the extended version of this).
Vol. 3: "So Ghetto" is the last time you'll hear Jay-Z and Premier together. "Dopeman" is another one of those allegorical "hey, rapping is like a criminal enterprise" joints. "It's Hot" is dope, but more relevant in retrospect because he disses 50 Cent on it. "Snoopy Track" has Juvenile on it (peep Juvenile's "Ha" remix for one of Jay-Z's worst performances). "Pop 4 Roc" is a pretty good posse cut, Sigel shines on it. "Big Pimpin", well, you know. "There's Been a Murder" is pretty tough. "Come and Get Me" is a personal favorite of mine.
Dynasty is pretty unfairly maligned. The intro is pure fire, don't let anyone tell you otherwise. "This Can't Be Life" is another one of my favorite Jay-Z songs ever. "Soon You'll Understand", "Squeeze 1st", "Stick 2 the Script", and "Where Have You Been" (this song is chilling) are the other highlights of this album, besides the singles. Oh, "You, Me, Him, Her" is a lot better live than it is on the album.
Blueprint 2... hrm. "A Dream" is kinda corny but cool, he rips "Hovi Baby", he and Rakim both come off pretty nice on "The Watcher 2" (beat sucks, tho). "What They Gonna Do" is wack. I personally am a fan of "All Around the World". Twista steals the show on "Poppin' Tags". "The Bounce" is pretty good. The second disc is much better. "Diamond Is Forever", "Guns & Roses", "U Don't Know (Remix)", "Meet the Parents" - he rips all of these. "Some How Some Way" is dope, but kinda zzz-inducing. "Some People Hate" is one of Kanye West's more slept-on beats. "Blueprint2" has a nice beat and a wack hook. "Nigga Please" is the best Neptunes beat on the album. "A Ballad for the Fallen Soldier" is also kinda sleepy. Of the bonus cuts, I only like "Bitches and Sisters" ("La La La" on Blueprint 2.1 is also dope).
The Black Album: There are a few wack beats on the album, but Jay-Z doesn't do anything wack on here, except for the chorus of the last song.
Dope non-album joints:
"In My Lifetime" and its remix
The original "Dead Presidents"
Jaz's "Originators"
Big L's "Da Graveyard"
The various flows on the S. Carter Collection mixtape
That remix with Mya
"People Talkin", a bonus cut on his live album
"Ignorant Shit"
"20 Bag Shorty"
"Anything"
"People's Court"
Extended version of "Big Pimpin"
"Hey Papi"
"Jigga My Nigga"
Beanie Sigel's "Still Got Love for You"
That long-ass Big L freestyle
Mary J Blige's "Love and Life"
dead prez's "Hell Yeah" remix
Freeway's "What We Do"
Talib Kweli's "Get By" remix
"Dear Summer"
Memphis Bleek's "Is That Yo Chick"
M.O.P.'s "4 Alarm Blaze", "Put it in the Air"
Outkast's "Flip Flop Rock"
That Punjabi MC joint
"Young Gs" off Puffy's first album
Biggie's "I Love the Dough"
Scarface's "Guess Who's Back"
That Slim Thug joint