While it's likely not the highest quality song in the sonic series, I can take a guess why it's so famous. I think it's important to note that most famous does not mean it is the best. I'm not entirely familiar with the melody, and I have a vague recollection of the actual song, but I do remember the song being very catchy and relatively high quality, and I'll attempt to infer why the song is so famous.
1) The song has an extremely distinct theme. This is a reason songs are considered popular rather than considered beautiful (entertainment vs. art). It's catchy, in the way some rhymes or popular music is catchy. The image of it is easy to remain in one's head, and can easily be associated with experiences that happened while the song was heard (nostalgia factor). But something tells me that this song had more than just catchiness, and had a bit of musical beauty to it as well, like, more than an adequate amount. My guess is many other Sonic songs were significantly more artful, but probably not quite as catchy most of the time. (I remember seeing someone play through the sonic 3Dblast game about 8 years back, the music is very high quality from what I remember of it, somewhat jazzy?).
2) The original Sonic the Hedgehog had an enormous audience in the 1990s, and the title screen theme and the theme for the opening stage are what people heard most. So it got viral exposure.
3) It was first like someone said, and set a precedent for the series that has been around for 25 years. It has been relegated to an iconic status. The first couple measures following the song's intro could easily be associated with the series as a whole, much like the opening motif the Super Mario Bros overworld song represents the Mario series. (Not sure how true this actually is, I'm not a sonic nut, it's likely not nearly at that level of association).
I know there's more to it, but I don't feel like typing something in the realm of TL;DR