Well of course here in Britain Red dwarf is something of a miner cultural icon, the series get rerun a lot, and lots of people, especially people who grew up in the nineties know the series very well.
I started watching them about the age of eleven and continued. I remember the hiatus between seasons 6 and 7 while craig charles was in jail and having violent disagreements with my friends about whether series 7 was any good or not.
The books also absolutely rock, although I didn't think backwards was a good end to the series, indeed you can check out my reviews of both infinity favours careful drivers and better than life over on fantasybookreview.co.uk.
I also got Mrs. Dark to read the books (the official recordings read by Chris barry), and she's now definitely a fan, though she did describe the humour in the series as "british humour" which might explain why it's less popular in the states I don't know, ---- obviously I grew up with them so to me they're just funny.
For those who say "the books can't be as good as the serie" my advice would be try them.
The books tell the story from the beginning, rather like the h2g2 books do, and do a dam good job, indeed in last human (one of the two alternative third books), they even provide a good ending to things.
So I'd definitely recommend both the series and the books to anyone enjoys scifi humour, indeed if your an h2g2 fan odds are you'd enjoy red dwarf too.
As to comparing them to startrek, --- well to me they really have nothing to do with each other. I did remember hearing that Patric Stewart is apparently a fan, and that the episode in season 6 (also covered in the book backwards), gunmen of the appocalypse was enspired by the tng episode fist full of datas, but other than that not a lot really, since at the end of the day red dwarf is intended as a comedy and startrek really isnt'.
With our dreaming and singing, Ceaseless and sorrowless we! The glory about us clinging Of the glorious futures we see,
Our souls with high music ringing; O men! It must ever be
That we dwell in our dreaming and singing, A little apart from ye. (Arthur O'Shaughnessy 1873.)