First things second

Before I go further with this review of stars in SF, I should state my criteria for deciding whether a star system is a good possibility for having habitable worlds:

• Spectral class: as we’ve seen, being a red dwarf is not a disqualifier for having a usable planet.  On the other hand, brown dwarfs are likely to be too cool (or rather, not hot enough), and those bigger and hotter than spectral class F5 or so are likely to be too short-lived to allow planets with ecosystems to develop during their lifespan.  Of course, we could find a terraformable world around such a star -- maybe it won’t be usable for more than a few million years, but that’s plenty of time on the human scale.
• Age: even a star that’s a G2V like our sun isn’t going to have an Earthlike world if it’s much less than 3 billion years old.  Earth as we know it didn’t develop overnight!  Conversely, stars that are more than 8 billion years old are probably “Population II” stars that have low metallicity.  This leads us to --
• Metallicity: if a star has few or no elements heavier than helium in its makeup, it probably never had the stuff necessary to make a planetary system.   It’s probably out there glowing in solitary splendour, with no orbiting attendants.

There can be other factors as well, which I will deal with as they come up, but those are the most important ones as I see them.