Fair enough, I do only really like a few of their songs, but the ones I do like are long term favourites.

One of their songs, 'Doctor! Doctor!' is one of those rare songs I heard that have blown me away on my first listening. I was actually lying dozing in the bath back in the day, with the radio on as background noise, when I first heard it. For some reason the song always brought to mind the now ancient arcade game 'Battlezone'. It was only when I gained access to YouTube that I actually got to view the song's video, and it does indeed feature a bleak landscape cluttered with geometric shapes (as does 'Battlezone'):-

http://www.youtube.com/watch?v=APyl6Cnbfzw

Downright eerie, that....

Anyway, I still continue listening to (some of) their music, and I suspect I'll never tire of it completely (like other artists such as Blondie, ELO, Status Quo etc.).

Anyone else like their music, or are they pretty much forgotten now?

One of my favourite 80's groups! I think if they are sort of forgotten it's because they have no interest in reuniting and don't tour or release new music like a lot of the other 80's acts.
But I definitely remember them and enjoy their music.

Yeah... I seem to remember reading something (somewhere!) about how the former group members don't rate the music they made in the Thompson Twins at all. They consider it all a joke. If I didn't just dream that, I think they're doing themselves a disservice. They put out some excellent songs imo.