Let's see...
Godzilla (1954) - This was actually among the last movies I saw, believe it or not. Bought a fan-subbed bootleg copy on VHS from The Outer Limits in Clifton, NJ somewhere around 2004 or 2005 and watched it in my college dorm room.
Godzilla, King of the Monsters - The 4th Godzilla movie I'd ever seen, when it played on one of TNT's Monstervision marathons back in March (I think) 1994. I remember staying up late that night to watch it. When the commercials were airing leading up to it, I knew instinctually that the B&W clips had to be from the first Godzilla movie (I also remember thinking Godzilla's ears were horns!

). I taped that Monstervision marathon and that VHS would be my only copy of this movie for YEARS. I eventually replaced it with the Simitar VHS (and, eventually, the Classic Media and Criterion DVDs and BD).
Godzilla Raids Again - Discovered the VHS in the Sci-Fi/Horror section of my favorite video rental store. Not sure when, exactly...some time between 1994 and 1998. I always thought it had a really cool cover. I didn't see the Japanese version until the Classic Media DVD was released a decade later. I actually always liked this movie, but IMO the Japanese version is WAY better than "Gigantis the Fire Monster".
King Kong vs. Godzilla - The first time I'd even heard of this movie was when I got the VHS (US Version) as a present for my birthday. Not sure when exactly, although I'm sure I could find a picture some place. Had to be March 1994, 1995, or 1996, though. I have yet to see the Japanese version.
Mothra vs. Godzilla - TNT's Monstervision, ~March 1994.
Ghidorah, The Three-Headed Monster - I'm, honestly, not exactly sure. It was probably between 1994 and 1996. It was another rental from the same video store I found GRA at (that place was AWESOME, they had EVERYTHING).
Monster Zero - TNT's Monstervision, ~March 1994. Not sure if anyone remembers this, but the version they played during Monstervision had the entirety of the second Planet X sequence cut. It goes from the Xillians taking Godzilla/Rodan and the characters noting that they must be flying near the speed of light, to a commercial, to them returning with the Xillians' ultimatum. I discovered G-Fan after this (my first issue was #16), so you can imagine my confusion to articles and letters referencing Godzilla and Rodan fighting Ghidorah on Planet X and pictures of Godzilla's little dance. I had no idea whatsoever that a sequence was missing until I caught the movie on WPIX (Channel 11 New York) one afternoon and they aired that scene - it was a revelation. Even now, I can barely recall those scenes...I saw the Monstervision version of this movie so many times between '94 and '98 that my memory of the version without that sequence overpowers the memories of the times I've seen the movie with that scene intact.
Ebirah, Horror of the Deep - Picked it up from the bargain bin in either K-Mart or Bradlees (a local version we used to have around here). Not sure when, but probably between '95 and '97.
Son of Godzilla - Rented from the awesome video store, some time between '94 and '97.
Destroy All Monsters - Summer, 1994. My family stumbled across a short-lived kaiju-themed store at the Boardwalk in Seaside Heights, NJ (behind the Funtime Pier). I was amazed at all the movies and imported Bandai figures the tiny place had. My eyes zeroed in DAM, and the guy made it irresistable by telling me it was this grand epic where "every monster on Earth fights King Ghidorah at the end". My parents bought it for me and I watched it as soon as we got home. It was exactly as awesome as promised.
All Monsters Attack - TNT's Monstervision, ~March 1994. I never liked this movie, even when I saw it for the first time. I just thought the kid was SO annoying. I did try to imitate it when I played (I remember at least once pretending I, too, had a radio to Monster Island), but overall I preferred GKOTM, MvG, and Monster Zero.
Godzilla vs. Hedorah - Rented from the awesome video store, some time between '94 and '97.
Godzilla vs. Gigan - Rented from the awesome video store, some time between '94 and '97. I remember picking up to this one and being kind of shocked by the picture on the back of Godzilla looking dead in front of Gigan and KG. Maybe as a result of this, in my mind this is one of the darkest Godzilla movies. This was the first one I saw where Godzilla really bled, so that probably factors into that impression.
Godzilla vs. Megalon - The first Godzilla movie I ever saw, some time around 1991. My cousins had this movie on VHS and my aunt would play it on TV while we were playing. This movie was the main reason I was at all familiar with Godzilla before I became a fan, I don't think I had any other exposure to the franchise besides one viewing of Mothra around the same time.
Godzilla vs. Mechagodzilla '74 - Purchased from the bargain bin in either K-Mart or Bradlees, some time between '94 and '97.
Terror of Mechagodzilla - The third Godzilla movie I'd ever seen, and the first one I saw after becoming a fan, in probably January or February 1994. Seeing I had become enamored with Godzilla (seemingly all of a sudden), my Dad took me to the local video store (not the awesome one, but a tiny one near our house) and rented the only Godzilla movie they had for me. It happened to be ToMG and...well...I didn't like it much. The problem was that the movie that made me a fan was Godzilla 1985, and sudden shift in tone, effects, and apparent quality (it wasn't a good copy) threw me off. It might've strangled my fandom then and there had TNT's Monstervision not aired shortly afterward - THAT really solidified it. Even though I recorded a copy on my Monstervision tape, being the last movie in the marathon and being after Godzilla's Revenge (which I didn't like) meant I didn't really watch this one much as a kid. There was a short time around '98 that I decided I liked Titanosaurus and wanted to edit together a Titanosaurus movie out of ToMG, but that was more or less the extent of my interest.