The self titled debut album by the Australian Pub band The Cockroaches, was released in 1987 on the independent record label, Regular Records, RML 53237.  Pop rock, bordering on rockabilly, this is a fun party/dance album.  Here is their cover of Double Shot (of my baby's love):

Songs of Leonard Cohen, his debut release on Columbia CS 9533, from 1967, will be a bit of a surprise if you have come to Leonard Cohen's music after the fame of Hallelujah, as his voice is still young. Not yet the whisky soaked deep voice of later recordings.
This singer/songwriter/poet, is truly a Canadian Icon and some of his songs are among my favourites.  Here is Sisters of Mercy followed by One of Us Cannot Be Wrong:

In his earlier music career, Leonard Cohen was much more popular in Europe than in North America.  Songs of Love and Hate, his 3rd studio album, reached #4 in the UK and only managed to climb to #145 on the billboard chart in the US.  Released on Columbia C-30103 in the US & CBS S-64090 in Europe (this copy is the latter) in 1971, I feel this an essential recording for any collector of Cohen.  Dark and beautiful at the same time.  This has two of his most enduring songs: Famous Blue Raincoat and Joan of Arc. 

Songs of Love & Hate, here is one of each:

Containing the most famous song Leonard Cohen ever wrote, perhaps the most famous song ever written period, Various Positions,  released in late 1984 in Canada and early 1985 elsewhere, did not break any records for sales at the time.  But at some point the song Hallelujah started to gain recognition.  With over 300 covers having been done of this song, it is hard to think that everyone has not heard at least one version; whether from the movie Shrek, Jeff Buckley's beautiful version or K.D. Lang at the Vancouver Olympics.  In a conversation in Paris with Bob Dylan, talking about recent songs they had written, Dylan showed Cohen lyrics to the song  I and I, he had just written.  Leonard asked how long it had taken him to write the song; "fifteen minutes" Dylan replied, then asked how long he had spent on Hallelujah, which he had just shown Bob.  Leonard replied "a couple of years" too embarrassed to tell him the truth of 5 years.  Filling note books of lyrics for the song, Leonard pared it down to around 80 verses, of which he finally edited down to this:

This album has many other great songs, including one of my favourites, Dance Me to the End of Love and Coming Back to You.  An album well worth owning.