I'll add a couple that others haven't mentioned:
No Doubt "Tragic Kingdom"
Yeah, yeah. I know. Gwen Stephani's gone kinda goofy in recent years, but this CD shows that they did have some musical chops behind them.
They Might Be Giants - "Flood"
Yeah, yeah. TMBG isn't for everyone. But this is still a heck of a CD. At the very least, it reintroduced "Istanbul (Not Constantinople)" to the listening public. An honorable mention to "Apollo 18" as well.
Barenaked Ladies "Gordon"
While they didn't hit it big in the US until 2000's "Maroon", BNL's debut CD was filled with songs that are still catchy a decade later.
The Refreshments "Fizzy, Fuzzy, Big and Buzzy"
Okay, I might be the only person who even remembers these guys, but I'll mention them anyway. The Refreshments were an Arizona band with a southwestern college rock type twang. Only one song of theirs ("Banditos") ever got much nationwide airplay (Although I heard a good chunk of the CD played on Denver radio) but the band seemed poised to explode... and then they vanished. (Okay, technically they released a second CD, broke up, and the lead singer formed a new band which is still around, but that's close enough for jazz.) Right now, the band is best known for the theme song to "King of the Hill". (And if you listen to the commentary on the pilot episode you can also hear Mike Judge talk about how the staff thought these guys would be huge.) But if you listen to the CD, you can hear a bunch of songs that'll make you say "Why didn't they ever play this on the radio?"
I'll give some "not classic, but still darn good" nods to INXS' "Welcome to Wherever You Are", "Empire Records", "Everyone Else is Doing It so Why Can't We?" by the Cranberries, and "Garbage" or "Version 2.0" by Garbage.
There are definitely classic tracks on both albums.