Everybody will have their own favourite but mine are (I can't just select one, I like all these fairly equally):
Greetings From Asbury Park, N.J. His debut, nearly 50 years old. Songs with great stories and a variety of moods giving a hint at what is to come. I prefer the original Blinded By The Light to M Mann's Earth Band, although I guess Bruce has done ok from the royalties.
The Wild, The Innocent & The E Street Shuffle I find this almost a continuation in style from his debut: more good stories, well-crafted tunes. Incident On 57th Street is possibly my desert-island Springsteen song.
These first two albums can take a bit of getting used to but I'd say they are worth it; I've listened to each - in full - probably a few hundred times.
Nebraska Fairly dark themes, stripped-back playing, more great stories. Atlantic City and Open All Night just nudge it as my favourites but the whole album is solid.
Tunnel Of Love Maybe not everyone's choice but again, full of well-written songs with great melodies. Has hints of Nebraska to my ears. One Step Up and All That Heaven Will Allow are a couple of my picks.
I like all of his albums in the period covered by those above except for, strangely, Darkness... from which I just can not find much enjoyable listening, except for maybe the more tuneful - for want of a better description - Badlands and Racing In The Street. I remember finding his first two albums a bit hard work and wondered what they were about but then found little bits that caught my interest and made me want to listen again. The same hasn't happened with Darkness... regardless of my perseverance.
I've not much experience of anything he's done post-ToL but really should investigate.