Umm… can’t remember having ever bought anything on vinyl.
Cassette – some kind of christian rock, probably Petra.
CD – Blackhawk’s “Love and gravity”
All-digital: Think this was a tie between corrs “talk on corners” and leahy “lakefield”
Vinyl: Remain in Light, Talking Heads
Cassette: Brothers in Arms, Dire Straits
CD: Chariots of Fire, Vangelis
All digital: None
78- Tumbling Tumbleweeds - Gene Aurtry
45 - I Saw Her Standing There - The Beatles
33.3 - Meet the Beatles
8 Track - Wee Tam - The Incredible String Band
Cassette - Workingman’s Dead - The Grateful Dead
CD - The Lady and the Unicorn - John Renbourn
Cassette: The Cranberries - Everybody Else Is Doing It, So Why Can’t We?
CD: Rage Against the Machine - Battle of Los Angeles & Green Day - Dookie (tie)
Digital: N/A, I’ve never spent money on that, nor do I have an iPod.
Vinyl: Johnny Cash ‘Live from San Quinten’
Tape: Guns and Roses ‘Appetite For Destruction’
CD: Black Crows ‘Shake your Money Maker’
Digital: Ween ‘The Mollusk’ (to replace a cd I broke)
LP- Queen, The Game
45- Alice Cooper, How You Gonna See Me Now
Cassette- Bauhaus, Burning From the Inside & Fugazi (I think)
CD- Depeche Mode (I don’t remember which album since I bought a ton of CD’s as soon as I got a CD player.
Digital - None yet.
Vinyl: I owned lots of records as a kid, but by the time I was buying my own music, I had entered the cassette era, and the only LPs I bought were those that were either much cheaper or much easier to find on vinyl than on cassette, and I don’t remember which one was the first. The first grown-up album I owned (given as a gift) was, IIRC, Simon & Garfunkel’s Greatest Hits.
Cassettes: Synchronicity (by The Police)
CD’s: I got my first CD player for Christmas (1991), along with a few CD’s I had asked for, including All Things Must Pass (by George Harrison), Seventh Sojourn (by The Moody Blues), There Goes Rhymin’ Simon (by Paul Simon), and Smiley Smile/Wild Honey (by the Beach Boys). The first CD’s I bought for myself were Daniel Amos and a few classical CD’s by Handel, Vivaldi, and Saint-Saens.
All digital: CD’s are all digital, aren’t they? Oh, you mean like a download? None; I’m still buying my music the old-fashioned way.
So how come the OP didn’t say anything about 8-track tapes? 
Vinyl 45 The Kinks Father Christmas
Vinyl LP The Rocky Horror Picture Show soundtrack
8 Track n/a There was an 8 track player on the hand-me-down quad system my brother-in-law gave me, but 8 track was long dead by then (c. 1986)
Cassette The Kinks State of Confusion
CD Elastica’s self-titled debut
Legally downloaded track for free The Queers Punk Rock Girls
Illegally downloaded track for free Believe or not, haven’t done it.
Purchased download haven’t done it yet
I’ve never owned a vinyl record. Unless you count the vinyl insert from the Bloom County collection, Billy and the Boingers.
My first cassette was, I believe, Rum, Sodomy, and the Lash by The Pogues.
My first CD was Iron Maiden’s Fear of the Dark.
The first entire album I ever purchased digitally was Marcy Playground’s third album, coincidentally titled MP3.
Vinyl 45: Beatles: not sure which song, likely Hey Jude…
Vinyl: Partridge Family Album (it’s true)
Cassette: AM/FM George Carlin (my parents wouldn’t let me have Class Clown)
CD: Steely Dan: Aja
Digital: Not sure: either Howard Stern Sound bytes or Dr. Demento songs off Napster.
Okay there have been revisions to the rules:
First single: A yellow 78 RPM – proudly bought with me birfday money of the QuickDraw McGraw Theme song with a B-side featuring Baba Looey
8-track–triple purchase: Little Criminals - Randy Newman; Meet the Roaches (Only Maggie and Terry on that one); Renaisance – can’t remember the title.
I don’t remember buying a first 45 (although I did).
Vinyl: Carpenters - Close To You (to learn a song for my first gig.) (Really)
First I bought for me was Three Dog Night - Naturally (A lot better, hunh)
8 Track: Leon Russell - Leon Live Really pissed my dad off when I told him I admired this guy (on the cover) because he is from Oklahoma, like me!
Cassette: Santana - Abraxas changed my life. The first cassette I bought was Johnny Winter - Saints and Sinners
CD: What does it say that I can distinctly remember all of the above but can’t remember the first CD I ever bought? I think it was Dire Straits - Brothers In Arms
Legal Digital Album(sic): Colonel Claypool’s Bucket Of Bernie’s Brains - The Big Eyeball in the Sky
Vinyl - Band on the Run - Paul McCartny & Wings
Cassette - Works - Emerson, Lake and Palmer
CD - Tales of Mystery and Imagination - The Alan Parsons Project
Digital - Haven’t bought a complete album, but my first digital purchase was Honeysuckle Blue by Drivin’ ‘n Cryin’
God, I am so gay.
VINYL: The Sound of Music (Mary Martin/Theodore Bikel Broadway recording)
CASSETTE: Yentl
CD: Miss Saigon and Songs from the Civil War (same time)
DIGITALl: Nothing yet, but when NAPSTER was legal I think my first download was Sting’s Desert Rose.
These are all the first I spent money on, not necessarily the first I owned.
First vinyl: American Pie - Don Mclean
First 8-track: Gary Puckett and the Union Gap Featuring Young Girl - Gary Puckett & the Union Gap
First Cassette: Van Halen - Van Halen
First CD: Nilsson, Schmilsson – Harry Nilsson
First Digital: I haven’t purchased any yet.
How do you guys remember that?
I remember the first 45, and that’s only because I didn’t have anything to play it on, but I loved the song – Only the Lonely by Roy Orbison.
I borrowed the neighbor boy’s portable record player to play it.
Can’t remember any of the rest. You guys are amazing!
Vinyl: Sugar Town by Nancy Sinatra
Cassette: Abbey Road by the Beatles
CD: Into the Gap by Thompson Twins
These were semi-important moments. I was always listening to my older Brother’s and Sister’s music. So starting to buy mine own was important in growing up. I was proud I was the first in the family to start a CD collection. Kind of silly I know, but important to a young man growing up.
Jim
Vinyl single: a 4-track Beatles single which included a cover of Roll Over Beethoven. I wish I still had it.
Vinyl Album: I think it was Guess Who’s Greatest Hits
8-track: ELP, Tarkus
Cassette: beats me - cassettes were a way to make albums last longer, or to listen to them in the car
CD: Heavy Weather, Weather Report. I bought this CD so I could use it to pick out a CD player… Birdland is a great test piece.
Downloads: free: Adrian Belew’s lost “lyrical” version of “I have a Dream”, which didn’t make the cut on King Crimson’s CD The Construkction of Light.
Downloads: paid: none.
Chronologically…
Vinyl 45: The Byrds, Eight Miles High
Vinyl LP: I think it was Beatles, Revolver. Might’ve been The Doors, Strange Days…Jeez, that was 40 years ago…
Cassette: Chicago II (with 25 or 6 to 4, Make Me Smile)
CD: Dunno. Joined a CD of the Month club, and got a batch on the same day. Most of it junk.
Digital Download (Napster)…hmmm…going with Dexy’s Midnight Runners, Come on Eileen