It seems like there have been two big waves of exposure to Tyrian: the original release and the subsequent re-release in the form of Tyrian 2000.
I was fortunate enough to play the original 1995 release of Tyrian when I was extremely young (one of the first games I ever played). I could barely read back then so I was only able to pick up the outline of the plot from the Data Cubes, but the game certainly cemented itself in my memory!
I first played the demo which stops after the level on planet Gyges (the boss of the Gyges level was pretty hard in the demo at least without modifying the ship). [Edit: I'm not sure if the planet was called Gyges in the demo, but it was pretty much the same.] I loved the game so much that I asked my parents to order the full game for me, and given how often we played the game it was probably one of the best commercial decisions my family ever made.
Given the early date at which I played the game, Tyrian is probably one of the oldest games that I continually return to replay (the other being Mega Man X); even today the pixel art in its unique style is gorgeous, too. I made a habit of playing the game on a desktop computer from early childhood all the way though high school. It really is a hidden gem, both in terms of game-play and presentation. Humour and idiosyncrasy aside, it doesn't get enough credit for its story which is really aided by the iconic and striking visuals. (Anyone else recall the horrifying skull on a pike after finishing Episode I?)
[Edit: The soundtrack is absolutely out of this world too! It has so much range, being fun and rock-centric when it needs to be but also eerie and strange when it needs to be, adding gravitas for the events of the game. From the unsettling medley of the title screen onward It helped me to become invested in what was going on and made me feel like I really was in a distant sector somewhere in the far future of the universe shooting up Microsol ships.]
I do think that if Tyrian were made today that it would be a massive hit, and to be honest there really should be an updated version or a sequel. I saw someone remake the first level in 3D, and that was amazing, but I'm not sure that I prefer it to pixel art as there are a number of fantastic modern games being made in that style today. Either way, a return to the far-future universe of Tyrian is long overdue, and I'd love nothing more than for this amazing series to reach a wider audience!