It has numerous Flash and Java iterations, and I’m sure there are downloadable versions as well (that would be nice!). I have no idea what it’s generally called, but the game called “SF Cave” at Fetchfido is similar: here.
Basically, you’re flying a ship through a cave and between/around some generic obstacles; it scrolls left-to-right and your only control is to “give it the gas”, causing the ship to shoot upward on the screen while continuing to scroll. The link above is the game I’m talking about, but I’m looking for something with a larger playable screen. Thanks!