To what extend are you aware of the wonderful world of chiptune music and video game music rearrangements? By video game music rearrangements I mean thinks like symphonic concerts (my favorite is "Symphonic Fantasies", which you can listen to on youtube and is much better than some others, like "Video Games Live" ), the Final Fantasy piano collections, ocremix.org, and the works fans put on youtube.

Anyway, what I'm really asking is, are those old game soundtracks actually any good, or do I just have no taste?

If you have no taste, you are not alone. Nabuo Uematsu is quite popular. Personally I found those exact videos quite annoying, though that might have to do with sound quality and some filters might improve them. I do, however, like the piano arrangements this one guy made to pieces from the same series: Burning Blood and a Legend 1 medley. I also love the Link's Awakening OST and this album, which has a similar (Game Boy) sound.

I think I have fairly poor taste in music.

What do you think is a good taste in music?

My first answer would be that the concept is quite silly. (That also seems politically correct to me)

My second answer would be that it's not about what music you like but about how varied your taste is. It seems to me that one gets more total amounts of enjoyment and different kinds of experiences from liking different kinds of music, and different qualities in music.

If you are interested in developing your taste, I'd suggest you listen to this Final Fantasy medley (I'm assuming you are familiar with the Final Fantasy music. For me the Chrono medley from the same concert was the first time I really appreciated symphonic music). Try to recognize the themes. That should be fun (at least it's for me) and you might like the piece better after having concentrated on it. You could then pay attention to different aspects like the variation in loudness (sometimes the music whispers, sometimes it's loud and impressive), which is something pop-music or chiptune don't really have. If you take a liking to this type of music you can then listen to something like Beethoven's 5th and notice that it's really the same type of music.