Your favorite LP nobody has ever heard of

Speaking of debut lps...and sort of along this thread...Graham Parker "howlin wind"...great brit r&b style pub rock... The Rumour was his backing band...those cats can groove...and once again... From '76!...great production by Nick Lowe

You want obscure?
Aliotta, Haynes and Jeremiah: Very nice wooden music group (Hit "Lake Shore Drive")
Silver Metre: Short lived Hard Rock/Psyc San Francisco band from 1970s. Members from Blue Cheer, Jeff Beck group et al.

Joe Cocker... A Luxury You Can Afford

lots of great picks, though i'd agree that many aren't especially obscure (who needs rules, right?). a few more:
love nut, bastards of melody--a power pop masterpiece with really big hooks and tight playing. great cover of "green tambourine". (the principal's subsequent band, myracle brah, is also excellent, if overly beatle-esque). available on spotify.
the neats, crash at crush--intense, loud folk rock not too far removed from rem. the singer has a really deep, cool voice. i've never seen this stuff on cd, but well worth tracking down.

Wow the Neats!...brings back memories...one of Boston's great enigmas..."another broken dream" from their debut LP has a killer bass line...also like label mates the Lyres...another forgotten band from this era...the Broadcasters